Chapter 3: IntegersContent check — Prealgebra, Chapter 3: Integers

Plot the numbers on a number line.

ⓐ $1$

ⓑ $\mathrm{-1}$

ⓒ $\mathrm{-4}$

Plot the numbers on a number line.

ⓐ $\mathrm{-4}$

ⓑ $4$

ⓐ $\mathrm{-1}$

Order each of the following pairs of numbers using $<$ or $\text{>.}$

ⓐ $15\_\_\_7$

ⓑ $\mathrm{-2}\_\_\_5$

ⓒ $\mathrm{-3}\_\_\_\mathrm{-7}$

ⓓ $5\_\_\_\mathrm{-17}$

Order each of the following pairs of numbers using $<$ or $\text{>.}$

ⓐ $8\_\_\_13$

ⓑ $3\_\_\_\mathrm{-4}$

ⓒ $\mathrm{-5}\_\_\_\mathrm{-2}$

ⓓ $9\_\_\_\mathrm{-21}$

Find the opposite of each number:

ⓐ $4$

ⓑ $\mathrm{-3}$

Find the opposite of each number:

ⓐ $8$

ⓑ $\mathrm{-5}$

Simplify:

$-\left(\mathrm{-1}\right)$

Simplify:

$-\left(\mathrm{-5}\right)$

Evaluate $-n:$

ⓐ $\text{when}n=4$

ⓑ $\text{when}n=\mathrm{-4}$

Evaluate: $-m:$

ⓐ $\text{when}m=11$

ⓑ $\text{when}m=\mathrm{-11}$

Simplify:

ⓐ $\left|12\right|$

ⓑ $-\left|\mathrm{-28}\right|$

Simplify:

ⓐ $\left|9\right|$

ⓑ $-\left|37\right|$

Evaluate:

ⓐ $\left|x\right|\text{when}x=$ $\mathrm{-17}$

ⓑ $\left|\text{−y}\right|\text{when}y=$ $\mathrm{-39}$

ⓒ $-$ $\left|m\right|\text{when}m=$ $22$

ⓓ $-$ $\left|p\right|\text{when}p=$ $\mathrm{-11}$

ⓐ $\left|y\right|\text{when}y=$ $\mathrm{-23}$

ⓑ $|-$ $y|\text{when}y=$ $\mathrm{-21}$

ⓒ $-$ $\left|n\right|\text{when}n=$ $37$

ⓓ $-$ $\left|q\right|\text{when}q=$ $\mathrm{-49}$

Fill in $\text{<},$ $\text{>},$ $\text{or}=$ $\text{for each of the following:}$

ⓐ $\left|\mathrm{-9}\right|\text{\_\_\_}-$ $\left|\mathrm{-9}\right|$

ⓑ $2\_\_\_-\left|\mathrm{-2}\right|$

ⓒ $\mathrm{-8}\_\_\_\left|\mathrm{-8}\right|$

ⓓ $-\left|\mathrm{-5}\right|\text{\_\_\_}\mathrm{-5}$

Fill in $\text{<},$ $\text{>},$ $\text{or}=$ for each of the following:

ⓐ $7\text{\_\_\_}-\left|\mathrm{-7}\right|$

ⓑ $-$ $\left|\mathrm{-11}\right|\text{\_\_\_}\mathrm{-11}$

ⓒ $\left|\mathrm{-4}\right|\text{\_\_\_}-$ $\left|\mathrm{-4}\right|$

ⓓ $\mathrm{-1}\text{\_\_\_}\left|\mathrm{-1}\right|$

Simplify:

ⓐ $|12-9|$

ⓑ $3\left|\mathrm{-6}\right|$

Simplify:

ⓐ $|27-16|$

ⓑ $9\left|\mathrm{-7}\right|$

Translate each phrase into an expression with integers:

ⓐ the opposite of positive nine

ⓑ the opposite of $\mathrm{-15}$

ⓒ negative twenty

ⓓ eleven minus negative four

Translate each phrase into an expression with integers:

ⓐ the opposite of negative nineteen

ⓑ the opposite of twenty-two

ⓒ negative nine

ⓓ negative eight minus negative five

Translate into an expression with integers:

The football team had a gain of $5\text{yards.}$

Translate into an expression with integers:

The scuba diver was $30\text{feet}$ below the surface of the water.

Locate Positive and Negative Numbers on the Number Line

For the following exercises, draw a number line and locate and label the given points on that number line.

ⓐ $2$

ⓑ $\mathrm{-2}$

ⓒ $\mathrm{-5}$

Locate Positive and Negative Numbers on the Number Line

For the following exercises, draw a number line and locate and label the given points on that number line.

ⓐ $\mathrm{-8}$

ⓑ $8$

ⓒ $\mathrm{-6}$

Order Positive and Negative Numbers on the Number Line

In the following exercises, order each of the following pairs of numbers, using $<$ or $\text{>.}$

ⓐ $9\text{\_\_}4$

ⓑ $\mathrm{-3}\text{\_\_}6$

ⓒ $\mathrm{-8}\text{\_\_}\mathrm{-2}$

ⓓ $1\text{\_\_}\mathrm{-10}$

Order Positive and Negative Numbers on the Number Line

In the following exercises, order each of the following pairs of numbers, using $<$ or $\text{>.}$

ⓐ $\mathrm{-5}\text{\_\_}1;$

ⓑ $\mathrm{-4}\text{\_\_}\mathrm{-9};$

ⓒ $6\text{\_\_}10;$

ⓓ $3\text{\_\_}\mathrm{-8}$

Find Opposites

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

ⓐ $2$

ⓑ $\mathrm{-6}$

Find Opposites

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

ⓐ $\mathrm{-8}$

ⓑ $1$

In the following exercises, simplify.

$-(\mathrm{-4})$

In the following exercises, simplify.

$-(\mathrm{-15})$

In the following exercises, evaluate.

$-m\text{when}$

ⓐ $m=3$

ⓑ $m=\mathrm{-3}$

In the following exercises, evaluate.

$-c\text{when}$

ⓐ $c=12$

ⓑ $c=\mathrm{-12}$

Simplify Expressions with Absolute Value

In the following exercises, simplify each absolute value expression.

ⓐ $\left|7\right|$

ⓑ $\left|\mathrm{-25}\right|$

ⓒ$\left|0\right|$

Simplify Expressions with Absolute Value

In the following exercises, simplify each absolute value expression.

ⓐ $\left|\mathrm{-32}\right|$

ⓑ $\left|\mathrm{-18}\right|$

ⓒ $\left|16\right|$

In the following exercises, evaluate each absolute value expression.

ⓐ $\left|x\right|\text{when}x=$ $\mathrm{-28}$

ⓑ $|-$ $u|\text{when}u=$ $\mathrm{-15}$

In the following exercises, evaluate each absolute value expression.

ⓐ $-$ $\left|p\right|\text{when}p=$ $19$

ⓑ $-$ $\left|q\right|\text{when}q=$ $\mathrm{-33}$

In the following exercises, fill in $\text{<},$ $\text{>},$ $\text{or}=$ to compare each expression.

ⓐ $\mathrm{-6}\text{\_\_}\left|\mathrm{-6}\right|$

ⓑ $-\left|\mathrm{-3}\right|\text{\_\_}\mathrm{-3}$

In the following exercises, fill in $\text{<},$ $\text{>},$ $\text{or}=$ to compare each expression.

ⓐ $\left|\mathrm{-3}\right|\text{\_\_}-\left|\mathrm{-3}\right|$

ⓑ $4\text{\_\_}-\left|\mathrm{-4}\right|$

In the following exercises, simplify each expression.

$\left|8-4\right|$

In the following exercises, simplify each expression.

$8\left|\mathrm{-7}\right|$

In the following exercises, simplify each expression.

$|15-$ $7|-$ $|14-$ $6|$

In the following exercises, simplify each expression.

$18-\left|2(8-3)\right|$

In the following exercises, simplify each expression.

$8(14-2|\mathrm{-2}|)$

Translate Word Phrases into Expressions with Integers

Translate each phrase into an expression with integers. Do not simplify.

ⓐ the opposite of $8$

ⓑ the opposite of $\mathrm{-6}$

ⓒ negative three

ⓓ $4$ minus negative $3$

Translate Word Phrases into Expressions with Integers

Translate each phrase into an expression with integers. Do not simplify.

ⓐ the opposite of $20$

ⓑ the opposite of $\mathrm{-5}$

ⓒ negative twelve

ⓓ $18$ minus negative $7$

Translate Word Phrases into Expressions with Integers

Translate each phrase into an expression with integers. Do not simplify.

a temperature of $6\text{degrees}$ below zero

Translate Word Phrases into Expressions with Integers

Translate each phrase into an expression with integers. Do not simplify.

an elevation of $40\text{feet}$ below sea level

Translate Word Phrases into Expressions with Integers

Translate each phrase into an expression with integers. Do not simplify.

a football play loss of $12\text{yards}$

Translate Word Phrases into Expressions with Integers

Translate each phrase into an expression with integers. Do not simplify.

a stock gain of $\text{\$3}$

Translate Word Phrases into Expressions with Integers

Translate each phrase into an expression with integers. Do not simplify.

a golf score one above par

Translate Word Phrases into Expressions with Integers

Translate each phrase into an expression with integers. Do not simplify.

Elevation The highest elevation in the United States is Mount McKinley, Alaska, at $\mathrm{20,320}\text{feet}$ above sea level. The lowest elevation is Death Valley, California, at $282\text{feet}$ below sea level. Use integers to write the elevation of:

ⓐ Mount McKinley

ⓑ Death Valley

Translate Word Phrases into Expressions with Integers

Translate each phrase into an expression with integers. Do not simplify.

State budgets In June, 2011, the state of Pennsylvania estimated it would have a budget surplus of $\text{\$540 million.}$ That same month, Texas estimated it would have a budget deficit of $\text{\$27 billion.}$ Use integers to write the budget:

ⓐ surplus

ⓑ deficit

Translate Word Phrases into Expressions with Integers

Translate each phrase into an expression with integers. Do not simplify.

Give an example of a negative number from your life experience.

Model the expression.

$2+4$

Model the expression.

$2+5$

Model the expression.

$\mathrm{-2}+(\mathrm{-4})$

Model the expression.

$\mathrm{-2}+(\mathrm{-5})$

Model the expression, and then simplify:

$2+\left(\mathrm{-4}\right)$

Model the expression, and then simplify:

$2+(\mathrm{-5})$

Model the expression, and then simplify:

$\left(\mathrm{-2}\right)+4$

Model the expression:

$\left(\mathrm{-2}\right)+5$

Model each addition.

ⓐ 3 + 4

ⓑ −1 + 4

ⓒ 4 + (−6)

ⓓ −2 + (−2)

ⓐ 5 + 1

ⓑ −3 + 7

ⓒ 2 + (−8)

ⓓ −3 + (−4)

Simplify each expression:

ⓐ $15+(\mathrm{-32})$

ⓑ $\mathrm{-19}+76$

Simplify each expression:

ⓐ $\mathrm{-55}+9$

ⓑ $43+(\mathrm{-17})$

Simplify the expression:

$\mathrm{-31}+(\mathrm{-19})$

Simplify the expression:

$\mathrm{-42}+(\mathrm{-28})$

Simplify the expression:

$\mathrm{-2}+5(\mathrm{-4}+7)$

Simplify the expression:

$\mathrm{-4}+2(\mathrm{-3}+5)$

Evaluate each expression for the given values:

$x+5\text{when}$

ⓐ $x=\mathrm{-3}\text{and}$

ⓑ $x=\mathrm{-17}$

Evaluate each expression for the given values: $y+7$ when

ⓐ $y=\mathrm{-5}$

ⓑ $y=\mathrm{-8}$

When $n=\mathrm{-8},$ evaluate

ⓐ $n+2$

ⓑ $-n+2$

$\text{When}y=$ $\mathrm{-9},$ $\text{evaluate}$

ⓐ $y+8$

ⓑ $-y+8.$

Evaluate the expression:

$a+$ $2b\text{when}a=$ $\mathrm{-19}\text{and}b=$ $14.$

Evaluate the expression:

$5p+$ $q\text{when}p=$ $4\text{and}q=$ $\mathrm{-7}.$

Evaluate:

${(x+y)}^2$ when $x=\mathrm{-15}$ and $y=29.$

Evaluate:

${(x+y)}^3$ when $x=\mathrm{-8}$ and $y=10.$

Translate and simplify the expression:

the sum of $\mathrm{-7}$ and $4$

Translate and simplify the expression:

the sum of $\mathrm{-8}$ and $\mathrm{-6}$

Translate and simplify:

the sum of $9$ and $\mathrm{-16},$ increased by $4.$

Translate and simplify:

the sum of $\mathrm{-8}$ and $\mathrm{-12},$ increased by $7.$

Model Addition of Integers

In the following exercises, model the expression to simplify.

$7+4$

Model Addition of Integers

In the following exercises, model the expression to simplify.

$\mathrm{-6}+(\mathrm{-3})$

Model Addition of Integers

In the following exercises, model the expression to simplify.

$\mathrm{-7}+5$

Model Addition of Integers

In the following exercises, model the expression to simplify.

$8+(\mathrm{-7})$

Simplify Expressions with Integers

In the following exercises, simplify each expression.

$\mathrm{-21}+(\mathrm{-59})$

Simplify Expressions with Integers

In the following exercises, simplify each expression.

$48+(\mathrm{-16})$

Simplify Expressions with Integers

In the following exercises, simplify each expression.

$\mathrm{-200}+65$

Simplify Expressions with Integers

In the following exercises, simplify each expression.

$2+(\mathrm{-8})+6$

Simplify Expressions with Integers

In the following exercises, simplify each expression.

$\mathrm{-14}+(\mathrm{-12})+4$

Simplify Expressions with Integers

In the following exercises, simplify each expression.

$135+$ $(\mathrm{-110})+$ $83$

Simplify Expressions with Integers

In the following exercises, simplify each expression.

$\mathrm{-32}+$ $24+$ $(\mathrm{-6})+$ $10$

Simplify Expressions with Integers

In the following exercises, simplify each expression.

$19+2(\mathrm{-3}+8)$

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

$x+8$ when

ⓐ $x=\mathrm{-26}$

ⓑ $x=\mathrm{-95}$

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

$y+(\mathrm{-14})$ when

ⓐ $y=\mathrm{-33}$

ⓑ $y=30$

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

When $a=\mathrm{-7},$ evaluate:

ⓐ $a+3$

ⓑ $-a+3$

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

When $c=\mathrm{-9},$ evaluate:

ⓐ $c+(\mathrm{-4})$

ⓑ $-c+(\mathrm{-4})$

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

$m+n$ when, $m=\mathrm{-15}$, $n=7$

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

$r\mathrm{-3}s$ when, $r=16$, $s=2$

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

${(a+b)}^2$ when, $a=\mathrm{-7}$, $b=15$

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

${(x+y)}^2$ when, $x=\mathrm{-3}$, $y=14$

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate each phrase into an algebraic expression and then simplify.

The sum of $\mathrm{-14}$ and $5$

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate each phrase into an algebraic expression and then simplify.

$8$ more than $\mathrm{-2}$

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate each phrase into an algebraic expression and then simplify.

$\mathrm{-10}$ added to $\mathrm{-15}$

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate each phrase into an algebraic expression and then simplify.

$6$ more than the sum of $\mathrm{-1}$ and $\mathrm{-12}$

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate each phrase into an algebraic expression and then simplify.

the sum of $10$ and $\mathrm{-19},$ increased by $4$

Add Integers in Applications

In the following exercises, solve.

Temperature The temperature in St. Paul, Minnesota was $\mathrm{-19}\text{°F}$ at sunrise. By noon the temperature had risen $\text{26°F.}$ What was the temperature at noon?

Add Integers in Applications

In the following exercises, solve.

Credit Cards Lupe owes $\text{\$73}$ on her credit card. Then she charges $\text{\$45}$ more. What is the new balance?

Add Integers in Applications

In the following exercises, solve.

Football A team lost $\text{3 yards}$ the first play. Then they lost $\text{2 yards,}$ gained $\text{1 yard,}$ and then lost $\text{4 yards.}$ What was the change in overall yardage over the four plays?

Add Integers in Applications

In the following exercises, solve.

Football The Rams took possession of the football on their own $\text{35-yard line.}$ In the next three plays, they lost $\text{12 yards,}$ gained $\text{8 yards,}$ then lost $\text{6 yards.}$ On what yard line was the ball at the end of those three plays?

Add Integers in Applications

In the following exercises, solve.

Scuba Diving A scuba diver swimming $\text{8 feet}$ below the surface dove $\text{17 feet}$ deeper; the pressure got to them and they rose five feet. What is their new depth?

Add Integers in Applications

In the following exercises, solve.

Stock Market The week of September 15, 2008, was one of the most volatile weeks ever for the U.S. stock market. The change in the Dow Jones Industrial Average each day was:

$$\begin{array}{cccccc}\text{Monday}\hfill & \mathrm{-504}\hfill & \text{Tuesday}\hfill & +142\hfill & \text{Wednesday}\hfill & \mathrm{-449}\hfill \\ \text{Thursday}\hfill & +410\hfill & \text{Friday}\hfill & +369\hfill & \end{array}$$

What was the overall change for the week?

Add Integers in Applications

In the following exercises, solve.

Explain why the sum of $\mathrm{-8}$ and $2$ is negative, but the sum of $8$ and $\mathrm{-2}$ and is positive.

Model the expression:

$6-4$

Model the expression:

$7-4$

Model the expression:

$\mathrm{-6}-(\mathrm{-4})$

Model the expression:

$\mathrm{-7}-(\mathrm{-4})$

Model the expression:

$\mathrm{-6}-4$

Model the expression:

$\mathrm{-7}-4$

Model the expression:

$6-(\mathrm{-4})$

Model the expression:

$7-(\mathrm{-4})$

Model each subtraction.

ⓐ 7 - (-8)

ⓑ -7 - (-2)

ⓒ 4 - 1

ⓓ -6 - 8

Model each subtraction.

ⓐ 4 - (-6)

ⓑ -8 - (-1)

ⓒ 7 - 3

ⓓ -4 - 2

Model each subtraction expression.

ⓐ $7-9$

ⓑ $\mathrm{-5}-(\mathrm{-9})$

Model each subtraction expression.

ⓐ $4-7$

ⓑ $\mathrm{-7}-(\mathrm{-10})$

Simplify each expression:

ⓐ $21-$ $13\text{and}21+$ $(\mathrm{-13})$

ⓑ $\mathrm{-11}-$ $7\text{and}\mathrm{-11}+$ $(\mathrm{-7})$

Simplify each expression:

ⓐ $15-$ $7\text{and}15+$ $(\mathrm{-7})$

ⓑ $\mathrm{-14}-$ $8\text{and}\mathrm{-14}+$ $(\mathrm{-8})$

Simplify each expression:

ⓐ $6-$ $(\mathrm{-13})\text{and}6+$ $13$

ⓑ $\mathrm{-5}-$ $(\mathrm{-1})\text{and}\mathrm{-5}+$ $1$

Simplify each expression:

ⓐ $4-$ $(\mathrm{-19})\text{and}4+$ $19$

ⓐ $\mathrm{-4}-$ $(\mathrm{-7})\text{and}\mathrm{-4}+$ $7$

Simplify the expression:

$\mathrm{-67}-(\mathrm{-38})$

Simplify the expression:

$\mathrm{-83}-(\mathrm{-57})$

Simplify the expression:

$8-(\mathrm{-3}-1)-9$

Simplify the expression:

$12-$ $(\mathrm{-9}-6)-$ $14$

Simplify the expression:

$6·2-$ $9·1-$ $8·9.$

Simplify the expression:

$2·5-3·7-4·9$

Evaluate each expression:

$y-7\text{when}$

ⓐ $y=5$

ⓑ $y=\mathrm{-8}$

Evaluate each expression:

$m-3\text{when}$

ⓐ $m=1$

ⓑ $m=\mathrm{-4}$

Evaluate each expression:

$17-k\text{when}$

ⓐ $k=19$

ⓑ $k=\mathrm{-19}$

Evaluate each expression:

$\mathrm{-5}-b\text{when}$

ⓐ $b=14$

ⓑ $b=\mathrm{-14}$

Translate and simplify:

ⓐ the difference of $14$ and $\mathrm{-23}$

ⓑ subtract $21$ from $\mathrm{-17}$

Translate and simplify:

ⓐ the difference of $11$ and $\mathrm{-19}$

ⓑ subtract $18$ from $\mathrm{-11}$

Araceli has $\text{\$75}$ in her checking account and writes a check for $\text{\$27}.$

ⓐ What is the balance after she writes the check?

ⓑ She writes a second check for $\text{\$50}.$ What is the new balance?

ⓒ The check for $\text{\$20}$ that she sent a charity was never cashed. What is the balance in Araceli’s checking account now?

Genevieve’s bank account was overdrawn and the balance is $-\text{\$78}.$

ⓐ She deposits a check for $\text{\$24}$ that she earned babysitting. What is the new balance?

ⓑ She deposits another check for $\text{\$49}.$ Is she out of debt yet? What is her new balance?

Model Subtraction of Integers

In the following exercises, model each expression and simplify.

$8-2$

Model Subtraction of Integers

In the following exercises, model each expression and simplify.

$\mathrm{-5}-(\mathrm{-1})$

Model Subtraction of Integers

In the following exercises, model each expression and simplify.

$\mathrm{-5}-4$

Model Subtraction of Integers

In the following exercises, model each expression and simplify.

$8-(\mathrm{-4})$

Simplify Expressions with Integers

In the following exercises, simplify each expression.

ⓐ $15-6$

ⓑ $15+(\mathrm{-6})$

Simplify Expressions with Integers

In the following exercises, simplify each expression.

ⓐ $44-28$

ⓑ $44+(\mathrm{-28})$

Simplify Expressions with Integers

In the following exercises, simplify each expression.

ⓐ $8-(\mathrm{-9})$

ⓑ $8+9$

Simplify Expressions with Integers

In the following exercises, simplify each expression.

ⓐ $27-(\mathrm{-18})$

ⓑ $27+18$

In the following exercises, simplify each expression.

$15-(\mathrm{-12})$

In the following exercises, simplify each expression.

$10-(\mathrm{-19})$

In the following exercises, simplify each expression.

$48-87$

In the following exercises, simplify each expression.

$31-79$

In the following exercises, simplify each expression.

$\mathrm{-31}-11$

In the following exercises, simplify each expression.

$\mathrm{-17}-42$

In the following exercises, simplify each expression.

$\mathrm{-103}-(\mathrm{-52})$

In the following exercises, simplify each expression.

$\mathrm{-45}-(\mathrm{-54})$

In the following exercises, simplify each expression.

$8-3-7$

In the following exercises, simplify each expression.

$\mathrm{-5}-4+7$

In the following exercises, simplify each expression.

$\mathrm{-14}-(\mathrm{-27})+9$

In the following exercises, simplify each expression.

$71+(\mathrm{-10})-8$

In the following exercises, simplify each expression.

$\mathrm{-16}-$ $(\mathrm{-4}+1)-$ $7$

In the following exercises, simplify each expression.

$(2-7)-(3-8)$

In the following exercises, simplify each expression.

$-$ $(6-8)-$ $(2-4)$

In the following exercises, simplify each expression.

$25-$ $[10-(3-12)]$

In the following exercises, simplify each expression.

$6\cdot 3-4\cdot 3-7\cdot 2$

In the following exercises, simplify each expression.

$5^2-6^2$

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression for the given values.

$x-6\text{when}$

ⓐ $x=3$

ⓑ $x=\mathrm{-3}$

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression for the given values.

$5-y\text{when}$

ⓐ $y=2$

ⓑ $y=\mathrm{-2}$

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression for the given values.

$4x^2-$ $15x+$ $1\text{when}x=$ $3$

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression for the given values.

$\mathrm{-12}-$ $5x^2\text{when}x=$ $6$

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate each phrase into an algebraic expression and then simplify.

ⓐ The difference of $3$ and $\mathrm{-10}$

ⓑ Subtract $\mathrm{-20}$ from $45$

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate each phrase into an algebraic expression and then simplify.

ⓐ The difference of $\mathrm{-6}$ and $9$

ⓑ Subtract $\mathrm{-12}$ from $\mathrm{-16}$

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate each phrase into an algebraic expression and then simplify.

ⓐ $8$ less than $\mathrm{-17}$

ⓑ $-24$ minus $37$

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate each phrase into an algebraic expression and then simplify.

ⓐ $21$ less than$6$

ⓑ $31$ subtracted from $\mathrm{-19}$

Subtract Integers in Applications

In the following exercises, solve the following applications.

Temperature One morning, the temperature in Urbana, Illinois, was $\text{28° Fahrenheit.}$ By evening, the temperature had dropped $\text{38° Fahrenheit.}$ What was the temperature that evening?

Subtract Integers in Applications

In the following exercises, solve the following applications.

Temperature On January 15, the high temperature in Anaheim, California, was $\text{84° Fahrenheit.}$ That same day, the high temperature in Embarrass, Minnesota was $\text{−12° Fahrenheit.}$ What was the difference between the temperature in Anaheim and the temperature in Embarrass?

Subtract Integers in Applications

In the following exercises, solve the following applications.

Football At the first down, the Warriors football team had the ball on their $\text{30-yard line.}$ On the next three downs, they gained $\text{2 yards,}$ lost $\text{7 yards,}$ and lost $\text{4 yards.}$ What was the yard line at the end of the third down?

Subtract Integers in Applications

In the following exercises, solve the following applications.

Checking Account John has $\text{\$148}$ in his checking account. He writes a check for $\text{\$83.}$ What is the new balance in his checking account?

Subtract Integers in Applications

In the following exercises, solve the following applications.

Checking Account Gina has $\text{\$210}$ in her checking account. She writes a check for $\text{\$250.}$ What is the new balance in her checking account?

Subtract Integers in Applications

In the following exercises, solve the following applications.

Checking Account Bill has a balance of $\text{−\$14}$ in his checking account. He deposits $\text{\$40}$ to the account. What is the new balance?

Subtract Integers in Applications

In the following exercises, solve the following applications.

Camping Rene is on an Alpine hike. The temperature is$-\text{7}\text{°}.$ Rene’s sleeping bag is rated “comfortable to $-\text{20}\text{°”.}$ How much can the temperature change before it is too cold for Rene’s sleeping bag?

Subtract Integers in Applications

In the following exercises, solve the following applications.

Explain why the difference of $9$ and $\mathrm{-6}$ is $15.$

Multiply:

ⓐ $\mathrm{-6}·8$

ⓑ $\mathrm{-4}(\mathrm{-7})$

ⓒ $9(\mathrm{-7})$

ⓓ $5·12$

Multiply:

ⓐ $\mathrm{-8}·7$

ⓑ $\mathrm{-6}(\mathrm{-9})$

ⓒ $7(\mathrm{-4})$

ⓓ $3·13$

Multiply.

ⓐ $\mathrm{-1}·9$

ⓑ $\mathrm{-1}·(\mathrm{-17})$

Multiply.

ⓐ $\mathrm{-1}·8$

ⓑ $\mathrm{-1}·(\mathrm{-16})$

Divide:

ⓐ $\mathrm{-42}÷6$

ⓑ $\mathrm{-117}÷(\mathrm{-3})$

Divide:

ⓐ $\mathrm{-63}÷7$

ⓑ $\mathrm{-115}÷(\mathrm{-5})$

Divide:

ⓐ $6÷(\mathrm{-1})$

ⓑ $\mathrm{-36}÷(\mathrm{-1})$

Divide:

ⓐ $28÷(\mathrm{-1})$

ⓑ $\mathrm{-52}÷(\mathrm{-1})$

Simplify:

$8(\mathrm{-3})+$ $5(\mathrm{-7})\mathrm{-4}$

Simplify:

$9(\mathrm{-3})+$ $7(\mathrm{-8})-$ $1$

Simplify:

ⓐ ${(\mathrm{-3})}^4$

ⓑ ${\mathrm{-3}}^4$

Simplify:

ⓐ ${(\mathrm{-7})}^2$

ⓑ $-7^2$

Simplify:

$17-4(8-11)$