iCoachMath.com: Examples on Solving Multi-Step Equations - Equations & Inequalities - (AL)
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Solved Examples

Curriculum: Alabama Course of Study   Click to change Curriculum

Topic: Equations & Inequalities  Click to change Topic

Lesson: 6: Solving Multi-Step Equations  Click to change Lesson

Click on a 'View Solution' below for other questions:
e   Solve for a using the graph shown.   e View Solution
e   Solve for p from the graph shown.   e View Solution
e   Tommy's microwave repair bill was $68. This included $13.6 for each hour of labor and $27.20 for parts. Solve the equation 27.20 + 13.6h = 68 to find the number of hours of labor.
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e   Solve for y from the graph shown.
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e   Solve: - 24 - 6d = 12   e View Solution
e   Marissa planned to distribute 2 chocolate bars each, to her 20 friends on her birthday. She distributed the chocolates she had and they were enough for only 16 of her friends. Solve the equation 16 + s2 = 20, and find out s, the number of chocolate bars she falls short of.   e View Solution
e   Nathan goes to school from his house, riding his bicycle at a speed of 8 minutes a mile. On the way, he takes a break for 8 minutes. He takes a total of 40 minutes to reach his school. Use the equation 8 + 8d = 40, to find d, the distance of the school from his house.
   e
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e   Mrs. Chris used 8 cups of sugar while preparing Apple pie and Chocolate cake for her daughter's birthday party. She used a total of 5 cups of sugar for the chocolate cake. The recipe of apple pie needs 17 cup of sugar per serving. Solve the equation 5 + s ( 17) = 8 to find s, the number of servings of apple pie she made.   e View Solution
e   A number decreased by 6 equals 4 times the number. Find the number.
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e   Sunny ate 45part of the cake that was eaten by Frank. If Sunny ate 200 gms, then how much did Frank eat?
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e   A volleyball team consists of 6 members. The sum of the heights of 2 members in the team is 320 cm. What will be the sum of the heights (in cm) of other 4 players, if the average height of the entire team equals 160 cm?
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e   What is the value of x, if (x - 9) + 9 = 18?
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e   Justin paid $3.95 for 5 pencils and 1 eraser. Find the cost of one pencil, if the cost of the eraser is $0.20.   e View Solution
e   If an object travels 2 yd per minute, then find the distance it will travel in half an hour.
   e
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e   The total capacity of a tank is 120 liters. What portion of the tank is full, if there are 80 liters of water in the tank at the moment?   e View Solution
e   Danielle bought a yard of fabric and paid $248, which is 34 of its labeled price. What is the labeled price, rounded to the nearest dollar?   e View Solution
e   The length of a rectangular house is 323 times its width. What is the width of the rectangle, if the length is 22 ft?   e View Solution
e   Solve: 3d - 1 = 5
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e   Solve: 7d + 36 = 8
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e   Solve: d5 + 6 = - 5   e View Solution
e   Solve: d7 - 5 = 7
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e   Solve: -7 - d5 = -9
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e   Every week, Matt's father gave him $7 to save. Matt had $15 before his father started giving him money and saved a total of $85. Solve the equation 15 + 7w = 85 to find w, the number of weeks his father gave him the money.
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e   Victor is a mobile salesman who is paid a daily allowance of $39, and $4 for every house call. Today he sets out to earn $107. Solve the equation, 39 + 4h = 107, to find h, the number of house calls he should make.
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e   Hanna's parents, to encourage her, promised to give her $900 if she would pass the high school finals and $60 more for every 'A' grade she would get in her subjects. Hanna received $1140 as her prize. Solve the equation, 900 + 60s = 1140, to find s, the number of subjects in which she got 'A' grade.   e View Solution
e   A truck driver drove a total distance of 1880 miles in a week. On the first day, he traveled a distance of 200 miles and on the rest of the days, he travels the same distance on each day. Solve the equation 200 + 6m = 1880, to find how many miles m, he traveled each day from the second day onwards.
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e   Jerald deposits $44 in his savings account every week. What will be his account balance after 2 weeks, if he now has $263 in his account?
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e   Ethan's allowance lets him save $7 per week. He wants to buy a music system with his savings. His parents agree to contribute $99 upfront. The music system costs $183. Solve the equation 7w + 99 = 183 and find the number of weeks he has to save money to buy the music system.
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e   A teacher wants to tape sheets of paper together to make a science banner 53 inches long. She has one sheet that is 23 inches long and all the other sheets are 5 inches long. Solve the equation 23 + 5s = 53, to find the number of sheets of paper 5 inches long required to prepare the banner.
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e   Sheela was reading a novel, which had 10 chapters. She spent 2 hour(s) reading the first chapter and took the same amount of time to read all the other chapters of the novel. She completed reading the novel in 29 hours. Solve the equation 2 + 9h = 29, to find h, the number of hours she spent reading each chapter other than the first one.
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e   Emily bought 3 bottles of Mayonnaise and a sandwich bread package worth $4. The total bill was $16. Solve the equation 4 + 3b = 16, to find the cost of each mayonnaise bottle.
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e   A camera was priced $215, 3 weeks ago. Its price decreased in equal amounts, each week, for 2 weeks. The camera is now priced $209. Solve the equation 215 - 2d = 209, to find d, the decrease in its price each week.
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e   Mr. Sam plans to build a Greenhouse with tinted glass panes. He buys 90 pieces of the glass panes from a wholesale store and gets a discount of $100 . The total bill comes to $1700. Solve the equation 90g - 100 = 1700 to find the cost of each glass pane, g.   e View Solution
e   The tallest person in the army is 7534 in. high. He is 612 in. taller than the shortest person. What is the height of the shortest person?   e View Solution
e   Solve -3x - 9 = 19 and round the value of x to the nearest hundredth.
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e   Solve 32.6x + 30.6 = 75.2 and round the value of x to the nearest tenth.
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e   In a small locality, 45 of the families are rich. If there are 24 rich families in the locality, find the total number of families in the locality.   e View Solution
e   Find the value of x, if 4x + 5 = 17.   e View Solution
e   4 times of 4 less than a number n is 8. Find the number n.
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e   A number z is multiplied by 3 and the result is decreased by 18 to give 6. Find z.
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e   A number n is multiplied by 8 and the result is increased by 5 to give 37. What is the value of n?
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e   A disc jockey must allow time for 4 commercials, each of the same duration, and has to play music for 20 minutes in every 32 minutes of time he gets. Solve the equation 20 + 4t = 32 to find the time for each commercial.
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e   Solve for m, if 13m - 5 = 7m.   e View Solution
e   Solve the equation 2(3n - 1) = 52.
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e   Find two consecutive integers such that the sum of the first integer and 3 times the second integer is equal to 59.
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e   The sum of 3 consecutive integers, x+4, x + 5 and x + 6 is 150. Find x.   e View Solution
e   Find the three consecutive even integers whose sum is 66.   e View Solution
e   A number n is increased by 9 and the result is divided by 4 to give 9. Find the number n.   e View Solution
e   Find two consecutive integers such that the sum of the first and 4 times the second is 39.   e View Solution
e   Find y, if 3(y + 2) = 6.
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e   Solve:
5m + 5 = 3(m - 5) +7   e
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e   Uncle Tommy gave $D to Francis & Sunny as a gift to be shared equally. Francis buys a book worth $50 and is still left with $250 worth of his share. Solve the equation D2 - 50 = 250 to find Uncle Tommy's gift value.   e View Solution
e   Solve:
16(y + 54) - 28 = - 4   e
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e   Mike gave 2 chocolates each to his 20 friends. Each chocolate costs him $0.6. Find the total cost of the chocolates.
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e   A pizza shop charges $4 for each pizza. Packing and delivery charge is $1 per order. Find the cost of ordering 8 pizzas.   e View Solution
e   Solve:
6x - 3x + 9 = 0   e
View Solution
e   Solve the equation 6(5f - 6) = 6(10f - 12).   e View Solution
e   Write an expression for the distance traveled by a cyclist in h hours at a speed of 19 km/h. Find the distance he travels in 4 hours.   e View Solution
e   What is the value of y in the equation 13(2y + 2) = 4?   e View Solution
e   Find the value of k in the equation 3(k - 15) = 12.   e View Solution
e   What is the value of y in the equation 3(y - 10) = 3(6 + 3)?   e View Solution
e   What is the value of x in the equation 15(9x + 5) = (x + 5)?
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e   Solve the equation 2v - 4 - 8 + 3v - v = 0.   e View Solution
e   Solve the equation t + 37 + 2t = 64.    e View Solution
e   Gary & Irena win a basket of Hershey bars at a fair and decide to share them equally. On the way home, Gary eats 3 bars while Irena eats none. Upon reaching home, Gary keeps 9 bars as his share. Find the number of bars 'H' that were in the basket initially, using the equation H2 - 3 = 9.
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e   Find y, if 5(y + 4) = 20.
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e   An ice skater plans to skate a distance of 240 miles at an average speed of 30 miles/hr. How long will it take him to skate the entire distance.
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e   Brad has 9 pencils less than thrice as many pencils as Matt does. How many pencils does Matt have, if Brad has 27 pencils?   e View Solution
e   244 is 10 more than 3 times a number n. Find n.   e View Solution
e   A number n is decreased by 4 and the result is multiplied by 6 to give 54. Find the number.   e View Solution
e   3 times a number n is added to the number n to give 24. What is the value of n?   e View Solution
e   A number n is increased by 6 and the result is multiplied by 2 to give 28. Find the number n.
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e   5 times a number P is increased by 7 to give 7. Find P.   e View Solution
e   Find the value of x, if the linear function 4x + 5 = 21.   e View Solution
e   Sheela planned to distribute 2 cookies each, to 18 friends on her birthday. She distributed the cookies she had and they were enough for only 14 of her friends. Solve the equation 14 + s2 = 18 and find out s, the number of cookies she falls short of.
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e   Solve: 5d - 2 = 13
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e   Twelve more than the product of a number a and 4 is equal to 28. Find the value of a.   e View Solution
e   What is the value of x, if 3x - 6 = 3?   e View Solution
e   What is the value of x, if 2(x - 2) + 9 = 3x + 16?   e View Solution
e   A number when increased by 9 equals 4 times the same number. Find the number.   e View Solution
e   Henry bought a book worth $86 and some pens worth $8 for each one. How many pens did he buy, if the total expenditure on them is $142?   e View Solution
e   Bill has $12 more than what Jim has. If they together have $32, then how much money does Bill have?
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e   Nathan has a set of chocolates. His brother has thrice as many as Nathan. If Nathan's brother has 12 chocolates, then how many chocolates does Nathan have.?
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e   Sunny bought oranges and pears. The number of oranges is 6 less than 3 times that of pears. If the number of oranges is 30, then find the number of pears.
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e   Henry ordered pizzas and burgers. The total cost of pizzas and burger is $12. Find the cost of pizzas, if the cost of the burgers is $5.
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e   Find the three consecutive numbers whose sum is 36.
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e   What is the value of x, if 5(x - 5) + 40 = 4(x - 4) + 28?   e View Solution
e   Solve: d4 - 2 = 4
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e   A pizza shop charges $4 for each pizza. Packing and delivery charge is $1 per order. Find the cost of ordering 4 pizzas.   e View Solution
e   Write an expression for the distance traveled by a cyclist in h hours at a speed of 19 km/h. Find the distance he travels in 3 hours.   e View Solution
e   Solve: d3 - 4 = - 3
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e   Solve: - 9 - 3d = 9   e View Solution
e   7 times a number S is increased by 9 to give 44. What is the value of S?
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e   An ice skater plans to skate a distance of 120 miles at an average speed of 10 miles/hr. How long will it take him to skate the entire distance.
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e   Lauren planned to distribute 3 chocolate bars each, to her 24 friends on her birthday. She distributed the chocolates she had and they were enough for only 18 of her friends. Solve the equation 18 + s3 = 24, and find out s, the number of chocolate bars she falls short of.   e View Solution
e   Andrew goes to school from his house, riding his bicycle at a speed of 7 minutes a mile. On the way, he takes a break for 7 minutes. He takes a total of 14 minutes to reach his school. Use the equation 7 + 7d = 14, to find d, the distance of the school from his house.
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e   Solve: 4d - 3 = 13
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e   Solve: 9d + 33 = 6
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e   Mrs. Nathan used 6 cups of sugar while preparing Apple pie and Chocolate cake for her daughter's birthday party. She used a total of 4 cups of sugar for the chocolate cake. The recipe of apple pie needs 15 cup of sugar per serving. Solve the equation 4 + s ( 15) = 6 to find s, the number of servings of apple pie she made.   e View Solution
e   Solve: d3 + 5 = - 3   e View Solution
e   Solve: d9 - 4 = 9
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e   Solve: -4 - d2 = -6
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e   Every week, Henry's father gave him $5 to save. Henry had $11 before his father started giving him money and saved a total of $66. Solve the equation 11 + 5w = 66 to find w, the number of weeks his father gave him the money.
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e   George is a mobile salesman who is paid a daily allowance of $29, and $3 for every house call. Today he sets out to earn $77. Solve the equation, 29 + 3h = 77, to find h, the number of house calls he should make.
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e   Christina's parents, to encourage her, promised to give her $800 if she would pass the high school finals and $100 more for every 'A' grade she would get in her subjects. Christina received $1200 as her prize. Solve the equation, 800 + 100s = 1200, to find s, the number of subjects in which she got 'A' grade.   e View Solution
e   A truck driver drove a total distance of 2640 miles in a week. On the first day, he traveled a distance of 300 miles and on the rest of the days, he travels the same distance on each day. Solve the equation 300 + 6m = 2640, to find how many miles m, he traveled each day from the second day onwards.
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e   Jimmy's microwave repair bill was $79.80. This included $13.3 for each hour of labor and $39.90 for parts. Solve the equation 39.90 + 13.3h = 79.80 to find the number of hours of labor.
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e   Justin's allowance lets him save $6 per week. He wants to buy a music system with his savings. His parents agree to contribute $96 upfront. The music system costs $204. Solve the equation 6w + 96 = 204 and find the number of weeks he has to save money to buy the music system.
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e   A disc jockey must allow time for 3 commercials, each of the same duration, and has to play music for 18 minutes in every 33 minutes of time he gets. Solve the equation 18 + 3t = 33 to find the time for each commercial.
   e
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e   Find the three consecutive even integers whose sum is 204.   e View Solution
e   Solve for m, if 12m - 2 = 9m.   e View Solution
e   3 times of 2 less than a number n is 12. Find the number n.
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e   A number z is multiplied by 3 and the result is decreased by 18 to give 9. Find z.
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e   Solve the equation 4(5n - 3) = 28.
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e   Find two consecutive integers such that the sum of the first integer and 3 times the second integer is equal to 63.
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e   In a small locality, 23 of the families are rich. If there are 18 rich families in the locality, find the total number of families in the locality.   e View Solution
e   Matt paid $3.50 for 4 pencils and 1 eraser. Find the cost of one pencil, if the cost of the eraser is $0.50.   e View Solution
e   A number decreased by 12 equals 5 times the number. Find the number.
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e   A teacher wants to tape sheets of paper together to make a science banner 85 inches long. She has one sheet that is 29 inches long and all the other sheets are 7 inches long. Solve the equation 29 + 7s = 85, to find the number of sheets of paper 7 inches long required to prepare the banner.
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e   The sum of 3 consecutive integers, x+1, x + 2 and x + 3 is 42. Find x.   e View Solution
e   Ursula was reading a novel, which had 7 chapters. She spent 3 hour(s) reading the first chapter and took the same amount of time to read all the other chapters of the novel. She completed reading the novel in 27 hours. Solve the equation 3 + 6h = 27, to find h, the number of hours she spent reading each chapter other than the first one.
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e   A number n is increased by 6 and the result is divided by 3 to give 6. Find the number n.   e View Solution
e   A camera was priced $237, 5 weeks ago. Its price decreased in equal amounts, each week, for 4 weeks. The camera is now priced $205. Solve the equation 237 - 4d = 205, to find d, the decrease in its price each week.
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e   If an object travels 4 ft per minute, then find the distance it will travel in half an hour.
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e   A number n is multiplied by 6 and the result is increased by 5 to give 17. What is the value of n?
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e   Mr. Edward plans to build a Greenhouse with tinted glass panes. He buys 60 pieces of the glass panes from a wholesale store and gets a discount of $200 . The total bill comes to $700. Solve the equation 60g - 200 = 700 to find the cost of each glass pane, g.   e View Solution
e   Uncle Henry gave $D to Ed & Justin as a gift to be shared equally. Ed buys a book worth $54 and is still left with $246 worth of his share. Solve the equation D2 - 54 = 246 to find Uncle Henry's gift value.   e View Solution
e   Jake & Christina win a basket of Hershey bars at a fair and decide to share them equally. On the way home, Jake eats 4 bars while Christina eats none. Upon reaching home, Jake keeps 8 bars as his share. Find the number of bars 'H' that were in the basket initially, using the equation H2 - 4 = 8.
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e   Find y, if 5(y + 4) = 20.
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e   Brian deposits $39 in his savings account every week. What will be his account balance after 5 weeks, if he now has $108 in his account?
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e   Solve:
4m + 5 = 2(m - 4) +6   e
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e   Solve:
14(y + 20) - 6 = - 2   e
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e   Ethan ate 23part of the cake that was eaten by Josh. If Ethan ate 60 gms, then how much did Josh eat?
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e   A volleyball team consists of 6 members. The sum of the heights of 3 members in the team is 510 cm. What will be the sum of the heights (in cm) of other 3 players, if the average height of the entire team equals 160 cm?
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e   What is the value of x, if (x - 7) + 7 = 16?
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e   Which of the following has the least value?   e View Solution
e   The total capacity of a tank is 70 liters. What portion of the tank is full, if there are 40 liters of water in the tank at the moment?   e View Solution
e   Jessica bought a yard of fabric and paid $222, which is 23 of its labeled price. What is the labeled price, rounded to the nearest dollar?   e View Solution
e   The length of a rectangular house is 545 times its width. What is the width of the rectangle, if the length is 116 ft? DDD View Solution
DDD Gary gave 4 chocolates each to his 20 friends. Each chocolate costs him $0.8. Find the total cost of the chocolates.
 DDD
View Solution
DDD Solve the equation 3(2f - 3) = 3(4f - 6). DDD View Solution
DDD Solve the equation 3v - 6 - 18 + 4v - v = 0. DDD View Solution
DDD Find two consecutive integers such that the sum of the first and 2 times the second is 14. DDD View Solution
DDD Solve:
4x - 2x + 4 = 0 DDD
View Solution
DDD What is the value of y in the equation 17(4y + 42) = 10? DDD View Solution
DDD Solve the equation t + 29 + 2t = 50.  DDD View Solution
DDD Tanya bought 4 bottles of Mayonnaise and a sandwich bread package worth $2. The total bill was $22. Solve the equation 2 + 4b = 22, to find the cost of each mayonnaise bottle.
 DDD
View Solution
DDD The tallest person in the army is 7712 in. high. He is 812 in. taller than the shortest person. What is the height of the shortest person? DDD View Solution
DDD Solve -3x - 6 = 13 and round the value of x to the nearest hundredth.
 DDD
View Solution
DDD Find the value of k in the equation 2(k - 13) = 8. DDD View Solution
DDD What is the value of y in the equation 5(y - 12) = 5(10 + 5)? DDD View Solution
DDD Solve 34.3x + 29.4 = 87.7 and round the value of x to the nearest tenth.
 DDD
View Solution
DDD Find y, if 3(y + 2) = 6.
 DDD
View Solution
DDD Twelve more than the product of a number a and 2 is equal to 18. Find the value of a. DDD View Solution
DDD What is the value of x in the equation 13(5x + 3) = (x + 3)?
 DDD
View Solution
DDD Find the value of x, if 6x + 7 = 31. DDD View Solution
DDD Find the value of x, if the linear function 7x - 8 = 13. DDD View Solution
DDD Rachel planned to distribute 4 chocolate bars each, to 32 friends on her birthday. She distributed the chocolate bars she had and they were enough for only 24 of her friends. Solve the equation 24 + s4 = 32 and find out s, the number of chocolate bars she falls short of.
 DDD
View Solution
DDD Solve: 4d - 3 = 13
 DDD
View Solution
DDD What is the value of x, if 2x - 4 = 4? DDD View Solution
DDD A number n is decreased by 2 and the result is multiplied by 5 to give 65. Find the number. DDD View Solution
DDD 5 times a number n is added to the number n to give 54. What is the value of n? DDD View Solution
DDD 203 is 17 more than 3 times a number n. Find n. DDD View Solution
DDD A number n is increased by 5 and the result is multiplied by 4 to give 40. Find the number n.
 DDD
View Solution
DDD 4 times a number P is increased by 6 to give 6. Find P. DDD View Solution
DDD 6 times a number S is increased by 5 to give 23. What is the value of S?
 DDD
View Solution
DDD Solve: d5 - 6 = - 5
 DDD
View Solution
DDD Nathan has a set of chocolates. His brother has thrice as many as Nathan. If Nathan's brother has 24 chocolates, then how many chocolates does Nathan have.?
 DDD
View Solution
DDD Chris bought cherrys and pears. The number of cherrys is 5 less than 4 times that of pears. If the number of cherrys is 35, then find the number of pears.
 DDD
View Solution
DDD Jason ordered pizzas and burgers. The total cost of pizzas and burger is $11. Find the cost of pizzas, if the cost of the burgers is $5.
 DDD
View Solution
DDD What is the value of x, if 3(x - 5) + 22 = 4x + 31? DDD View Solution
DDD A number when increased by 15 equals 4 times the same number. Find the number. DDD View Solution
DDD Solve:
2 = 23(6y - 9)
 DDD
View Solution
DDD Francis has $6 more than what Jeff has. If they together have $18, then how much money does Francis have?
 DDD
View Solution
DDD Josh bought a book worth $95 and some pens worth $7 for each one. How many pens did he buy, if the total expenditure on them is $130? DDD View Solution
DDD What is the value of x, if 4(x - 4) + 24 = 3(x - 3) + 15? DDD View Solution
DDD Jake has 15 stamps less than thrice as many stamps as Nathan does. How many stamps does Nathan have, if Jake has 45 stamps? DDD View Solution
DDD Solve: 3a + 2(a + 4) = -2  DDD View Solution
DDD What is the value of x, if 7x + 16 = 3x + 40?
 DDD
View Solution
DDD Find the three consecutive numbers whose sum is 33.
 DDD
View Solution
DDD Solve:
13(6a + 12) - 13 = 9 DDD
View Solution
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