Solved Examples and Worksheet for Simplifying Linear Expressions

Q1Simplify: 127m - 12m
A. 115m
B. 115
C. 127m
D. 139m

Solutions
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Step: 1
127m - 12m
  [Original expression.]
Step: 2
(127 - 12)m
  [Use distributive property.]
Step: 3
= 115m
  [Subtract.]
Correct Answer is :   115m
Q2Which of the following expressions is equivalent to the expression 5 + 2(2 + s)?
A. 8 + 2s
B. 10 + 2s
C. 9 + 2s
D. 11 + 2s

Solutions
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Step: 1
5 + 2(2 + s)
  [Original expression.]
Step: 2
= 5 + 2(2) + 2(s)
  [Use the distributive property of addition.]
Step: 3
= 5 + 4 + 2s
  [Multiply.]
Step: 4
= 9 + 2s
  [Combine like terms.]
Correct Answer is :   9 + 2s
Q3Which of the following expressions is the simplified form of 2x + 3x(5 + y)?
A. 20xy
B. 17x + 3(x + y)
C. 17x + 3xy
D. 17x + 15 + 3y

Solutions
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Step: 1
2x + 3x(5 + y)
  [Original expression.]
Step: 2
= 2x + 3x(5) + 3x(y)
  [Use the distributive property of addition.]
Step: 3
= 2x + 15x + 3xy
  [Multiply.]
Step: 4
= (2 + 15)x + 3xy
  [Use the distributive property of addition.]
Step: 5
= 17x + 3xy
  [Simplify inside the grouping symbols.]
Correct Answer is :   17x + 3xy
Q4Which of the following is the simplest form of the expression given below?
(a + 3 - 3a - 3 + 2a - 3 + 7a)
A. - 7a - 3
B. 7a + 3
C. - 7a + 3
D. 7a - 3

Solutions
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Step: 1
(a + 3 - 3a - 3 + 2a - 3 + 7a)
  [Original expression.]
Step: 2
= (a - 3a + 2a + 7a) + (3 - 3 - 3)
  [Use the commutative property of addition to reorder the terms.]
Step: 3
= 7a - 3
  [Combine like terms.]
Step: 4
Among the choices, the expression 7a - 3 is the simplified form of the expression.
Correct Answer is :   7a - 3
Q5Simplify: - 4p + 6p
A. 10
B. 2
C. 2p
D. 10p

Solutions
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Step: 1
-4p + 6p
  [Original expression.]
Step: 2
-4(p) + 6(p) = (-4 + 6)p
  [Use distributive property.]
Step: 3
= 2p
  [Simplify.]
Correct Answer is :   2p
Q6Simplify 8 + 12m - 10.
A. 12m - 2
B. 2m
C. 2m + 12
D. None of the above

Solutions
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Step: 1
8 + 12m - 10 = 12m + 8 - 10
  [Arrange like terms.]
Step: 2
= 12m + (8 - 10)
  [Use associative property.]
Step: 3
= 12m - 2
  [Simplify like terms.]
Correct Answer is :   12m - 2
Q7Simplify 4a + b + 3a - 5b.

A. 4ab
B. 7a - 4b
C. 7a - 5b
D. 7b + 4a

Solutions
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Step: 1
4a + b + 3a - 5b
  [Original expression.]
Step: 2
= 4a + 3a + b - 5b
  [Arrange like terms.]
Step: 3
= (4a + 3a) + (b - 5b)
  [Use associative property.]
Step: 4
= 7a - 4b
  [Combine like terms.]
Correct Answer is :   7a - 4b
Q8Simplify the expression.
8(a + 9b) + 8(2b)

A. 10a + 88b
B. 8a + 88b
C. 9a + 88b
D. 8a + 86b

Solutions
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Step: 1
8(a + 9b) + 8(2b)
  [Original expression.]
Step: 2
= 8a + 72b + 16b
  [Use the distributive property.]
Step: 3
= 8a + (72 + 16)b
  [Use the distributive property to combine like terms.]
Step: 4
= 8a + 88b
  [Simplify.]
Step: 5
The simplified form of the expression is 8a + 88b.
Correct Answer is :   8a + 88b
Q9Simplify the expression 48p + p.

A. 50p
B. 48p
C. 51p
D. 49p

Solutions
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Step: 1
48p + p
  [Original expression.]
Step: 2
= 48p + 1p
  [Use the identity property of multiplication.]
Step: 3
= (48 + 1)p
  [Use the distributive property to combine like terms.]
Step: 4
= 49p
  [Simplify.]
Step: 5
The simplified form of the expression is 49p.
Correct Answer is :   49p
Q10Simplify the expression.
4s + 5t + s
A. 5s + 6t
B. 6s + 5t
C. 5s + 5t
D. 4s + 5t

Solutions
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Step: 1
4s + 5t + s
  [Original expression.]
Step: 2
= 4s + s + 5t
  [Use commutative property.]
Step: 3
= (4s + s) + 5t
  [Use associative property.]
Step: 4
= 5s + 5t
  [Simplify within the grouping symbol.]
Correct Answer is :   5s + 5t
Q11Simplify:
43a + 23b + a
A. 23a + 44b
B. 43a +24b
C. 44a + 23b
D. None of the above

Solutions
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Step: 1
43a + 23b + a
  [Original expression.]
Step: 2
= 43a + a + 23b
  [Use commutative property.]
Step: 3
= (43a + a) + 23b
  [Use associative property.]
Step: 4
= 44a + 23b
  [Simplify within the grouping symbols.]
Correct Answer is :   44a + 23b
Q12Simplify the expression.
3s + 4t + s

A. 4s + 4t
B. 4s + 5t
C. 3s + 4t
D. 5s + 4t

Solutions
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Step: 1
3s + 4t + s
  [Original expression.]
Step: 2
= 3s + s + 4t
  [Use commutative property.]
Step: 3
= (3s + s) + 4t
  [Use associative property.]
Step: 4
= 4s + 4t
  [Simplify within the grouping symbol.]
Correct Answer is :   4s + 4t
Q13Simplify:
268m - 32m
A. 268m
B. 236m
C. 236
D. 300m

Solutions
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Step: 1
268m - 32m
  [Original expression.]
Step: 2
(268 - 32)m
  [Use distributive property.]
Step: 3
= 236m
  [Subtract.]
Correct Answer is :   236m

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