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2 x + 4 y 5 when
x = 7 , y = 8

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Simplify Expressions by Combining Like Terms

In the following exercises, identify the coefficient of each term.

In the following exercises, identify the like terms.

3 n , n 2 , 12 , 12 p 2 , 3 , 3 n 2

12 and 3 , n 2 and 3 n 2

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5 , 18 r 2 , 9 s , 9 r , 5 r 2 , 5 s

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In the following exercises, identify the terms in each expression.

11 x 2 + 3 x + 6

11 x 2 , 3 x , 6

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In the following exercises, simplify the following expressions by combining like terms.

7 p + 6 + 5 p 4

12 p + 2

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Translate an English Phrase to an Algebraic Expression

In the following exercises, translate the following phrases into algebraic expressions.

the sum of 8 and 12

8 + 12

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the difference of x and 4

x 4

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the difference of x and 3

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the product of 6 and y

6 y

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Adele bought a skirt and a blouse. The skirt cost $15 more than the blouse. Let b represent the cost of the blouse. Write an expression for the cost of the skirt.

b + 15

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Marcella has 6 fewer boy cousins than girl cousins. Let g represent the number of girl cousins. Write an expression for the number of boy cousins.

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Add and Subtract Integers

Use Negatives and Opposites of Integers

In the following exercises, order each of the following pairs of numbers, using<or>.


6 ___ 2
−7 ___ 4
−9 ___ −1
9 ___ −3

> < < >

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−5 ___ 1
−4 ___ −9
6 ___ 10
3 ___ −8

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In the following exercises,, find the opposite of each number.

−8 1

8 −1

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In the following exercises, simplify.

In the following exercises, simplify.

m when
m = 3
m = −3

−3 3

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p when
p = 6
p = −6

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Simplify Expressions with Absolute Value

In the following exercises,, simplify.

| 7 | | −25 | | 0 |

7 25 0

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| 5 | | 0 | | −19 |

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In the following exercises, fill in<,>, or = for each of the following pairs of numbers.


−8 ___ | −8 |
| −2 | ___ −2

< =

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| −3 | ___ | −3 |
4 ___ | −4 |

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In the following exercises, simplify.

8 ( 14 2 | −2 | )

80

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In the following exercises, evaluate.

| x | when x = −28

28 15

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| y | when y = −37
| z | when z = −24

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Add Integers

In the following exercises, simplify each expression.

140 + ( −75 ) + 67

132

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−32 + 24 + ( −6 ) + 10

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Subtract Integers

In the following exercises, simplify.

15 6 15 + ( −6 )

9 9

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12 9 12 + ( −9 )

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8 ( −9 ) 8 + 9

17 17

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4 ( −4 ) 4 + 4

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In the following exercises, simplify each expression.

−15 ( −28 ) + 5

18

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−16 ( −4 + 1 ) 7

−20

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−15 ( −6 + 4 ) 3

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Multiply Integers

In the following exercises, multiply.

Divide Integers

In the following exercises, divide.

Simplify Expressions with Integers

In the following exercises, simplify each expression.

−8 ( −2 ) 3 ( −9 )

43

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−7 ( −4 ) 5 ( −3 )

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−10 ( −4 ) ÷ ( −8 )

−5

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−8 ( −6 ) ÷ ( −4 )

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Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

x + 8 when
x = −26
x = −95

−18 −87

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y + 9 when
y = −29
y = −84

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When b = −11 , evaluate:
b + 6
b + 6

−5 17

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When c = −9 , evaluate:
c + ( −4 )
c + ( −4 )

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p 2 5 p + 2 when
p = −1

8

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q 2 2 q + 9 when q = −2

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6 x 5 y + 15 when x = 3 and y = −1

38

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3 p 2 q + 9 when p = 8 and q = −2

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Translate English Phrases to Algebraic Expressions

In the following exercises, translate to an algebraic expression and simplify if possible.

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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