#### Solved Examples and Worksheet for Solving Linear Equations in One Variable

Q1Solve q - 85 = - 17.

A. 101
B. 68
C. - 68
D. 102

Step: 1
q - 85 = - 17
[Original equation.]
Step: 2
q - 85 + 85 = - 17 + 85
Step: 3
q = 68
[Simplify.]
Q2Joe bought a shirt for $6 less than the original price. If he paid$36 for the shirt, then what was the original price?
A. $36 B.$216
C. $30 D.$42

Step: 1
Let x be the price on the tag.
Step: 2
The price Joe paid for the shirt = $(x - 6). Step: 3 x - 6 = 36 [Write an equation.] Step: 4 x - 6 + 6 = 36 + 6 [Add 6 to both sides.] Step: 5 x = 42 [Simplify.] Step: 6 The price on the tag is$42.
Correct Answer is :   $42 Q3The computer science department had 27 students in 2002. If 13 of these students failed, then how many students graduated? A. 14 B. 40 C. 7 D. 21 Step: 1 Let s be the number of students, who graduated. Step: 2 s + 13 = 27 [Write an equation.] Step: 3 s + 13 - 13 = 27 - 13 [Subtract 13 from each side.] Step: 4 s = 14 [Simplify.] Step: 5 The number of students who graduated is 14. Correct Answer is : 14 Q4Solve 27 + q = - 18. A. 45 B. - 45 C. - 50 D. - 55 Step: 1 27 + q = - 18 [Original equation.] Step: 2 27 + q - 27 = - 18 - 27 [Subtract 27 from each side.] Step: 3 q = - 45 [Simplify.] Correct Answer is : - 45 Q5The sum of 25 and another number is 32. What is the number? A. 32 B. 7 C. 6 D. 57 Step: 1 Let a be the another number. Step: 2 25 + a = 32 [Original equation.] Step: 3 25 + a - 25 = 32 - 25 [Subtract 25 from each side.] Step: 4 a = 7 [Simplify.] Step: 5 The other number is 7. Correct Answer is : 7 Q6Solve 4475 + k = 4000. A. 475 B. - 4950 C. 4950 D. - 475 Step: 1 4475 + k = 4000 [Original equation]. Step: 2 4475 + k - 4475 = 4000 - 4475 [Subtract 4475 from each side.] Step: 3 k = - 475 [Simplify.] Correct Answer is : - 475 Q7Which of the following is a solution of the equation x - 37 = 26? A. 73 B. 26 C. 63 D. 64 Step: 1 x - 37 = 26 [Original equation.] Step: 2 x - 37 + 37 = 26 + 37 [Add 37 on both sides.] Step: 3 x = 63 [Simplify.] Step: 4 So, 63 is the solution of the equation. Correct Answer is : 63 Q8What is the value of the variable p in the equation p - (- 5) = - 5? A. - 10 B. - 9 C. - 12 D. - 11 Step: 1 p - (- 5) = - 5 [Original equation.] Step: 2 p + 5 = - 5 [Use subtraction rule to simplify.] Step: 3 p + 5 - 5 = - 5 - 5 [Subtract 5 from each side.] Step: 4 p = - 10 [Simplify.] Step: 5 The value of the variable p in the equation is - 10. Correct Answer is : - 10 Q9Solve the equation a + 12 = 23. A. a = 11 B. a = 16 C. a = 21 D. a = 6 Step: 1 a + 12 = 23 [Original equation.] Step: 2 a + 12 - 12 = 23 - 12 [Subtract 12 from each side.] Step: 3 a = 11 [Simplify.] Correct Answer is : a = 11 Q10What is the value of p in the equation p - 17 = 45? A. 62 B. 68 C. 56 D. 50 Step: 1 p - 17 = 45 [Original equation.] Step: 2 p - 17 + 17 = 45 + 17 [Add 17 on both sides.] Step: 3 p = 62 [Simplify.] Step: 4 The value of the variable p in the equation is 62. Correct Answer is : 62 Q11Solve for x in the equation x + 17 = 59. A. 42 B. 47 C. 37 D. 50 Step: 1 x + 17 = 59 [Original equation.] Step: 2 x + 17 - 17 = 59 - 17 [Subtract 17 from each side.] Step: 3 x = 42 [Simplify.] Correct Answer is : 42 Q12Solve - a4 = 4. A. - 19 B. 15 C. - 16 D. 14 Step: 1 - a4 = 4 [Original equation.] Step: 2 (- 4) × - a4 = (- 4) × (4) [Multiply each side by - 4.] Step: 3 a = - 16 [Simplify.] Correct Answer is : - 16 Q13Solve x- 4 = - 5. A. 22 B. 20 C. - 20 D. - 22 Step: 1 x- 4 = - 5 [Original equation.] Step: 2 x- 4 × (- 4) = - 5 × (- 4) [Multiply each side by - 4.] Step: 3 x = 20 [Simplify.] Correct Answer is : 20 Q14Mr.John owns one-fourth part of a property. If the value of his share is$1,300, what is the total value of the property?
A. $6,225 B.$5,200
C. $8,250 D.$7,200

Step: 1
Let p be the total value of the property.
Step: 2
p4 = 1300
[Write an equation.]
Step: 3
p4 × 4 = 1300 × 4
[Multiply each side by 4.]
Step: 4
p = 5200
[Simplify.]
Step: 5
Total value of the property is $5,200. Correct Answer is :$5,200
Q15Jim drove his car to get to the beach. Gasoline costs about $2 per gallon. For his trip, Jim spent$100 on gasoline. How many gallons of gas did he use?
A. 46 gallons
B. 50 gallons
C. 52 gallons
D. 48 gallons

Step: 1
Let p be the gallons of gasoline consumed for Jim's journey.
Step: 2
100 = 2 × p
[Write an equation.]
Step: 3
1002 = 2 × p2
[Divide each side by 2.]
Step: 4
50 = p
[Simplify.]
Step: 5
So, 50 gallons of gasoline were consumed for Jim's journey.
Correct Answer is :   50 gallons