2.2 Evaluate, Simplify, and Translate Expressions

Substituting values into an expression, spotting terms, coefficients, and like terms worth combining, and turning word phrases into algebraic form.

Prealgebra 2e, 2.2 Evaluate, Simplify, and Translate Expressions

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79 exercises

2.2 Exercise 1

Before you get started, take this readiness quiz.

Is $n \div 5$ an expression or an equation?
If you missed this problem, review the reference.

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2.2 Exercise 2

Simplify $4^{5} .$
If you missed this problem, review the reference.

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2.2 Exercise 3

Simplify $1 + 8 \cdot 9 .$
If you missed this problem, review the reference.

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2.2 Exercise 5

Evaluate:

$y + 4 \text{when}$

ⓐ $y = 6$
ⓑ $y = 15$

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2.2 Exercise 6

Evaluate:

$a - 5 \text{when}$

ⓐ $a = 9$
ⓑ $a = 17$

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2.2 Exercise 8

Evaluate:

$8 x - 3 , \text{when}$

ⓐ $x = 2$
ⓑ $x = 1$

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2.2 Exercise 9

Evaluate:

$4 y - 4 , \text{when}$

ⓐ $y = 3$
ⓑ $y = 5$

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2.2 Exercise 11

Evaluate:

$x^{2} \text{when} x = 8 .$

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2.2 Exercise 12

Evaluate:

$x^{3} \text{when} x = 6 .$

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2.2 Exercise 14

Evaluate:

$2^{x} \text{when} x = 6 .$

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2.2 Exercise 15

Evaluate:

$3^{x} \text{when} x = 4 .$

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2.2 Exercise 17

Evaluate:

$2 x + 5 y - 4 \text{when} x = 11 \text{and} y = 3$

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2.2 Exercise 18

Evaluate:

$5 x - 2 y - 9 \text{when} x = 7 \text{and} y = 8$

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2.2 Exercise 20

Evaluate:

$3 x^{2} + 4 x + 1 \text{when} x = 3 .$

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2.2 Exercise 21

Evaluate:

$6 x^{2} - 4 x - 7 \text{when} x = 2 .$

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2.2 Exercise 22

Identify each term in the expression $9 b + 15 x^{2} + a + 6 .$ Then identify the coefficient of each term.

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2.2 Exercise 23

Identify all terms in the given expression, and their coefficients:

$4 x + 3 b + 2$

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2.2 Exercise 24

Identify all terms in the given expression, and their coefficients:

$9 a + 13 a^{2} + a^{3}$

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2.2 Exercise 25

Identify the like terms:

ⓐ $y^{3} , 7 x^{2} , 14 , 23 , 4 y^{3} , 9 x , 5 x^{2}$
ⓑ $4 x^{2} + 2 x + 5 x^{2} + 6 x + 40 x + 8 x y$

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2.2 Exercise 26

Identify the like terms in the list or the expression:

$9 , 2 x^{3} , y^{2} , 8 x^{3} , 15 , 9 y , 11 y^{2}$

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2.2 Exercise 27

Identify the like terms in the list or the expression:

$4 x^{3} + 8 x^{2} + 19 + 3 x^{2} + 24 + 6 x^{3}$

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2.2 Exercise 29

Simplify:

$7 x + 9 + 9 x + 8$

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2.2 Exercise 30

Simplify:

$5 y + 2 + 8 y + 4 y + 5$

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2.2 Exercise 32

Simplify:

$3 x^{2} + 9 x + x^{2} + 5 x$

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2.2 Exercise 33

Simplify:

$11 y^{2} + 8 y + y^{2} + 7 y$

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2.2 Exercise 34

Translate each word phrase into an algebraic expression:

ⓐ the difference of $20$ and $4$
ⓑ the quotient of $10 x$ and $3$

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2.2 Exercise 35

Translate the given word phrase into an algebraic expression:

ⓐ the difference of $47$ and $41$
ⓑ the quotient of $5 x$ and $2$

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2.2 Exercise 36

Translate the given word phrase into an algebraic expression:

ⓐ the sum of $17$ and $19$
ⓑ the product of $7$ and $x$

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2.2 Exercise 37

Translate each word phrase into an algebraic expression:

ⓐ Eight more than $y$
ⓑ Seven less than $9 z$

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2.2 Exercise 38

Translate each word phrase into an algebraic expression:

ⓐ Eleven more than $x$
ⓑ Fourteen less than $11 a$

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2.2 Exercise 39

Translate each word phrase into an algebraic expression:

ⓐ $19$ more than $j$
ⓑ $21$ less than $2 x$

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2.2 Exercise 40

Translate each word phrase into an algebraic expression:

ⓐ five times the sum of $m$ and $n$
ⓑ the sum of five times $m$ and $n$

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2.2 Exercise 41

Translate the word phrase into an algebraic expression:

ⓐ four times the sum of $p$ and $q$
ⓑ the sum of four times $p$ and $q$

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2.2 Exercise 42

Translate the word phrase into an algebraic expression:

ⓐ the difference of two times $x \text{and 8}$
ⓑ two times the difference of $x \text{and} 8$

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2.2 Exercise 43

The height of a rectangular window is $6$ inches less than the width. Let $w$ represent the width of the window. Write an expression for the height of the window.

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2.2 Exercise 44

The length of a rectangle is $5$ inches less than the width. Let $w$ represent the width of the rectangle. Write an expression for the length of the rectangle.

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2.2 Exercise 45

The width of a rectangle is $2$ meters greater than the length. Let $l$ represent the length of the rectangle. Write an expression for the width of the rectangle.

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2.2 Exercise 46

Blanca has dimes and quarters in her purse. The number of dimes is $2$ less than $5$ times the number of quarters. Let $q$ represent the number of quarters. Write an expression for the number of dimes.

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2.2 Exercise 47

Geoffrey has dimes and quarters in his pocket. The number of dimes is seven less than six times the number of quarters. Let $q$ represent the number of quarters. Write an expression for the number of dimes.

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2.2 Exercise 48

Lauren has dimes and nickels in her purse. The number of dimes is eight more than four times the number of nickels. Let $n$ represent the number of nickels. Write an expression for the number of dimes.

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