Solved Examples and Worksheet for Evaluating Algebraic Expressions

Q1Which of the following values of m, when substituted in the expression 5m + 5, gives a result of 150 ?
A. 34
B. 26
C. 29
D. None of the above

Solutions
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Step: 1
5m + 5 = 5(34) + 5
  [Substitute 34 for m.]
Step: 2
= 170 + 5
  [Simplify the expression.]
Step: 3
= 175 ≠ 150
  [Add.]
Step: 4
5m + 5 = 5(26) + 5
  [Substitute 26 for m.]
Step: 5
= 130 + 5
  [Simplify the expression.]
Step: 6
= 135 ≠ 150
  [Add.]
Step: 7
5m + 5 = 5(29) + 5
  [Substitute 29 for m.]
Step: 8
= 145 + 5
  [Simplify the expression.]
Step: 9
= 150
  [Add.]
Step: 10
The value of m which gives the result 150 is 29.
Correct Answer is :   29
Q2Find the value of (2m)3, if m = - 3.
A. -206
B. 206
C. -216
D. 216

Solutions
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Step: 1
(2m)3
  [Original expression.]
Step: 2
= (2 x -3)3
  [Replace the variable with the value, given.]
Step: 3
= 23 x -33
  [Since (ab)n = an x bn.]
Step: 4
= 8 x -27
  [Evaluate the powers.]
Step: 5
= - 216
  [Multiply.]
Correct Answer is :   -216
Q3Evaluate the expression 5x + 4y, for x = 4 and y = 2.

A. 15
B. 28
C. 12
D. 96

Solutions
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Step: 1
5x + 4y
  [Original expression.]
Step: 2
= 5(4) + 4(2)
  [Replace x with 4 and y with 2.]
Step: 3
= 20 + 8
  [Multiply 5 with 4; 4 with 2.]
Step: 4
= 28
  [Add 20 and 8.]
Correct Answer is :   28
Q4Find the value of 5x - 4y, for x = 9 and y = 2.
A. 40
B. 37
C. 47
D. None of the above

Solutions
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Step: 1
5x - 4y
  [Original expression.]
Step: 2
= 5(9) - 4(2)
  [Replace x with 9 and y with 2.]
Step: 3
= 45 - 8
  [Multiply 5 and 9; 4 and 2.]
Step: 4
= 37
  [Subtract 8 from 45.]
Correct Answer is :   37
Q5Evaluate the expression a(16 - b), for a = 4 and b = 4.

A. 50
B. 48
C. 58
D. 53

Solutions
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Step: 1
a(16 - b)
  [Original expression.]
Step: 2
= 4(16 - 4)
  [Replace a with 4 and b with 4.]
Step: 3
= 4(12)
  [Subtract 4 from 16.]
Step: 4
= 48
  [Multiply 4 and 12.]
Correct Answer is :   48
Q6Evaluate the expression 14(xy + 4), for x = 6, y = 4.
A. 7
B. 17
C. 9
D. None of the above

Solutions
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Step: 1
14(xy + 4)
  [Original expression.]
Step: 2
= 14(6(4) + 4)
  [Replace x with 6 and y with 4.]
Step: 3
= 14(24 + 4)
  [Multiply 6 and 4.]
Step: 4
= 14(28)
  [Add 24 and 4.]
Step: 5
= 7
  [Divide 28 by 4.]
Correct Answer is :   7
Q7What is the value of the expression (x - 1)4, if x = 5?

A. 20
B. 1280
C. 51
D. 256

Solutions
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Step: 1
(x - 1)4
  [Original expression.]
Step: 2
= (5 - 1)4
  [Substitute 5 for x.]
Step: 3
= (4) 4
  [Evaluate the expression in the grouping.]
Step: 4
= 256
  [Evaluate the exponent.]
Step: 5
The value of the expression (x - 1)4 for x = 5 is 256.
Correct Answer is :   256
Q8Evaluate the expression y + (z3 ), for y = 42 and z = 6.

A. 42
B. 2
C. 6
D. 44

Solutions
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Step: 1
y + (z3 )
  [Original expression.]
Step: 2
= 42 + (63)
  [Replace the variables with their values.]
Step: 3
= 42 + 2
  [Simplify.]
Step: 4
= 44
  [Add.]
Step: 5
The value of the expression y + (z3 ) for y = 42 and z = 6, is 44.
Correct Answer is :   44
Q9Find the perimeter(P) of a rectangle whose length(l) is 12 cm and width(w) is 11 cm using the formula P = 2(l + w).

A. 47 cm
B. 46 cm
C. 23 cm
D. 48 cm

Solutions
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Step: 1
The formula for the perimeter of a rectangle, P = 2(l + w).
Step: 2
The perimeter of the rectangle P = 2( 12 cm + 11 cm).
  [Substitute the values for l = 12 cm and w = 11 cm]
Step: 3
= 2(23 cm) = 46 cm.
Step: 4
So, the perimeter of the rectangle is 46 cm.
Correct Answer is :   46 cm
Q10Find the area(A) of a square of side(s) = 45 ft using the formula A = s × s.
A. 2026 ft2
B. 2024 ft2
C. 2025 ft2
D. 2027 ft2

Solutions
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Step: 1
The formula for the area of a square, A = s × s
Step: 2
The area of the square = 45 ft × 45 ft
  [Substitute the value for s = 45 ft]
Step: 3
= 2025 ft2
  [Multiply 45 by 45]
Step: 4
So, the area of the square of side length 45 ft is 2025 ft2.
Correct Answer is :   2025 ft2
Q11Find the area(A) of a rectangle with length(l) = 32 in. and width(w) = 31 in. using the formula A = lw.

A. 993 in.2
B. 992 in.2
C. 994 in.2
D. 991 in.2

Solutions
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Step: 1
The formula for the area of a rectangle, A = lw.
Step: 2
The area of the rectangle = 32 in × 31 in
  [Substitute the values for l = 32 in and w = 31 in]
Step: 3
= 992 in.2
Correct Answer is :   992 in.2
Q12A truck traveled at a rate (r) of 55 miles per hour for 2 hours. Find the distance traveled using the equation d = rt

A. 105 mi.
B. 110 mi.
C. 53 mi.
D. 27 mi.

Solutions
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Step: 1
The formula for distance, d = rt.
Step: 2
d =55 × 2
  [Substitute the values for r = 55 and t = 2]
Step: 3
So, the distance travelled = 110 mi.
Correct Answer is :   110 mi.

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