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Use Variables and Algebraic Symbols

In the following exercises, translate from algebra to English.

16 9

16 minus 9, the difference of sixteen and nine

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28 ÷ 4

28 divided by 4, the quotient of twenty-eight and four

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( 2 ) ( 7 )

2 times 7, the product of two and seven

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14 < 21

fourteen is less than twenty-one

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36 19

thirty-six is greater than or equal to nineteen

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y 1 > 6

y minus 1 is greater than 6, the difference of y and one is greater than six

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2 18 ÷ 6

2 is less than or equal to 18 divided by 6; 2 is less than or equal to the quotient of eighteen and six

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In the following exercises, determine if each is an expression or an equation.

Simplify Expressions Using the Order of Operations

In the following exercises, simplify each expression.

In the following exercises, simplify using the order of operations.

3 + 8 · 5 ( 3 + 8 ) · 5

43 55

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2 + 6 · 3 ( 2 + 6 ) · 3

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2 3 12 ÷ ( 9 5 )

5

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3 2 18 ÷ ( 11 5 )

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( 6 + 10 ) ÷ ( 2 + 2 )

4

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3 ( 1 + 9 · 6 ) 4 2

149

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5 ( 2 + 8 · 4 ) 7 2

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2 [ 1 + 3 ( 10 2 ) ]

50

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Evaluate an Expression

In the following exercises, evaluate the following expressions.

x 2 + 3 x 7 when x = 4

21

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6 x + 3 y 9 when
x = 6 , y = 9

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( x y ) 2 when
x = 10 , y = 7

9

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( x + y ) 2 when x = 6 , y = 9

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a 2 + b 2 when a = 3 , b = 8

73

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r 2 s 2 when r = 12 , s = 5

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2 l + 2 w when
l = 15 , w = 12

54

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2 l + 2 w when
l = 18 , w = 14

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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.

x 3 , 8 x , 14 , 8 y , 5 , 8 x 3

x 3 and 8 x 3 , 14 and 5

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6 z , 3 w 2 , 1 , 6 z 2 , 4 z , w 2

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9 a , a 2 , 16 , 16 b 2 , 4 , 9 b 2

16 and 4 , 16 b 2 and 9 b 2

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3 , 25 r 2 , 10 s , 10 r , 4 r 2 , 3 s

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

15 x 2 + 6 x + 2

15 x 2 , 6 x , 2

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10 y 3 + y + 2

10 y 3 , y , 2

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

7 u + 2 + 3 u + 1

10 u + 3

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10 a + 7 + 5 a 2 + 7 a 4

22 a + 1

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7 c + 4 + 6 c 3 + 9 c 1

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3 x 2 + 12 x + 11 + 14 x 2 + 8 x + 5

17 x 2 + 20 x + 16

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5 b 2 + 9 b + 10 + 2 b 2 + 3 b 4

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Translate an English Phrase to an Algebraic Expression

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

the difference of 14 and 9

14 9

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the difference of 19 and 8

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the product of 9 and 7

9 · 7

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the quotient of 36 and 9

36 ÷ 9

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the quotient of 42 and 7

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the sum of 8x and 3 x

8 x + 3 x

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the quotient of y and 3

y 3

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eight times the difference of y and nine

8 ( y 9 )

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seven times the difference of y and one

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Eric has rock and classical CDs in his car. The number of rock CDs is 3 more than the number of classical CDs. Let c represent the number of classical CDs. Write an expression for the number of rock CDs.

b 4

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The number of girls in a second-grade class is 4 less than the number of boys. Let b represent the number of boys. Write an expression for the number of girls.

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Greg has nickels and pennies in his pocket. The number of pennies is seven less than twice the number of nickels. Let n represent the number of nickels. Write an expression for the number of pennies.

2 n 7

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Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.

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Everyday math

Car insurance Justin’s car insurance has a $750 deductible per incident. This means that he pays $750 and his insurance company will pay all costs beyond $750. If Justin files a claim for $2,100.

  1. how much will he pay?
  2. how much will his insurance company pay?

$750 $1,350

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Home insurance Armando’s home insurance has a $2,500 deductible per incident. This means that he pays $2,500 and the insurance company will pay all costs beyond $2,500. If Armando files a claim for $19,400.

  1. how much will he pay?
  2. how much will the insurance company pay?
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Writing exercises

Explain the difference between an expression and an equation.

Answers may vary

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Why is it important to use the order of operations to simplify an expression?

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Explain how you identify the like terms in the expression 8 a 2 + 4 a + 9 a 2 1 .

Answers may vary

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Explain the difference between the phrases “4 times the sum of x and y ” and “the sum of 4 times x and y .”

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Self check

Use this checklist to evaluate your mastery of the objectives of this section.

A table is shown that is composed of four columns and six rows. The header row reads, from left to right, “I can …”, “Confidently”, “With some help” and “No – I don’t get it!”. The phrases in the first column read “use variables and algebraic symbols.”, “simplify expressions using the order of operations.”, “evaluate an expression.”, “identify and combine like terms.”, and “translate English phrases to algebraic expressions.”

After reviewing this checklist, what will you do to become confident for all objectives?

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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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