3.2 Add Integers

Before you get started, take this readiness quiz.

Evaluate $x + 8$ when $x = 6 .$
If you missed this problem, review the reference.

Before you get started, take this readiness quiz.

Simplify: $8 + 2 \left(5 + 1\right) .$
If you missed this problem, review the reference.

Before you get started, take this readiness quiz.

Translate the sum of $3$ and negative $7$ into an algebraic expression.
If you missed this problem, review the reference

Simplify:

1. ⓐ $19 + \left(−47\right)$
2. ⓑ $−32 + 40$

Simplify each expression:

1. ⓐ $15 + \left(−32\right)$
2. ⓑ $−19 + 76$

Simplify each expression:

1. ⓐ $−55 + 9$
2. ⓑ $43 + \left(−17\right)$

Simplify: $−14 + \left(−36\right) .$

Simplify the expression:

$−31 + \left(−19\right)$

Simplify the expression:

$−42 + \left(−28\right)$

Simplify: $−5 + 3 \left(−2 + 7\right) .$

Simplify the expression:

$−2 + 5 \left(−4 + 7\right)$

Simplify the expression:

$−4 + 2 \left(−3 + 5\right)$

Evaluate each expression for the given values:

$x + 5 \text{when}$

1. ⓐ $x = −3 \text{and}$
2. ⓑ $x = −17$

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

1. ⓐ $y = −5$
2. ⓑ $y = −8$

When $n = −8 ,$ evaluate

1. ⓐ $n + 2$
2. ⓑ $- n + 2$

$\text{When} y = −9 , \text{evaluate}$

1. ⓐ $y + 8$
2. ⓑ $- y + 8 .$

Evaluate the expression:

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

Evaluate the expression:

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

Evaluate:

$\left(x + y\right)^{2}$ when $x = −15$ and $y = 29 .$

Evaluate:

$\left(x + y\right)^{3}$ when $x = −8$ and $y = 10 .$

Translate and simplify: the sum of $−9$ and $5 .$

Translate and simplify the expression:

the sum of $−7$ and $4$

Translate and simplify the expression:

the sum of $−8$ and $−6$

Translate and simplify: the sum of $8$ and $−12 ,$ increased by $3 .$

Translate and simplify:

the sum of $9$ and $−16 ,$ increased by $4 .$

Translate and simplify:

the sum of $−8$ and $−12 ,$ increased by $7 .$

The temperature in Buffalo, NY, one morning started at $7 \text{degrees}$ below zero Fahrenheit. By noon, it had warmed up $12 \text{degrees} .$ What was the temperature at noon?

The temperature in Chicago at 5 A.M. was $10 \text{degrees}$ below zero Celsius. Six hours later, it had warmed up $\text{14 degrees Celsius}.$ What is the temperature at 11 A.M.?

A scuba diver was swimming $\text{16 feet}$ below the surface and then dove down another $\text{17 feet}.$ What is her new depth?

A football team took possession of the football on their $\text{42}-\text{yard line}.$ In the next three plays, they lost $\text{6 yards},$ gained $\text{4 yards},$ and then lost $\text{8 yards}.$ On what yard line was the ball at the end of those three plays?

The Bears took possession of the football on their $\text{20}-\text{yard line}.$ In the next three plays, they lost $\text{9 yards},$ gained $\text{7 yards},$ then lost $\text{4 yards}.$ On what yard line was the ball at the end of those three plays?

The Chargers began with the football on their $\text{25}-\text{yard line}.$ They gained $\text{5 yards},$ lost $\text{8 yards}$ and then gained $\text{15 yards}$ on the next three plays. Where was the ball at the end of these plays?

Simplify each expression.

$−21 + \left(−59\right)$

Simplify each expression.

$48 + \left(−16\right)$

Simplify each expression.

$−200 + 65$

Simplify each expression.

$2 + \left(−8\right) + 6$

Simplify each expression.

$−14 + \left(−12\right) + 4$

Simplify each expression.

$135 + \left(−110\right) + 83$

Simplify each expression.

$−32 + 24 + \left(−6\right) + 10$

Simplify each expression.

$19 + 2 \left(−3 + 8\right)$

Evaluate each expression.

$x + 8$ when

1. ⓐ $x = −26$
2. ⓑ $x = −95$

Evaluate each expression.

$y + \left(−14\right)$ when

1. ⓐ $y = −33$
2. ⓑ $y = 30$

Evaluate each expression.

When $a = −7 ,$ evaluate:

1. ⓐ $a + 3$
2. ⓑ $- a + 3$

Evaluate each expression.

When $c = −9 ,$ evaluate:

1. ⓐ $c + \left(−4\right)$
2. ⓑ $- c + \left(−4\right)$

Evaluate each expression.

$m + n$ when, $m = −15$, $n = 7$

Evaluate each expression.

$r −3 s$ when, $r = 16$, $s = 2$

Evaluate each expression.

$\left(a + b\right)^{2}$ when, $a = −7$, $b = 15$

Evaluate each expression.

$\left(x + y\right)^{2}$ when, $x = −3$, $y = 14$

Translate each phrase into an algebraic expression and then simplify.

The sum of $−14$ and $5$

Translate each phrase into an algebraic expression and then simplify.

$8$ more than $−2$

Translate each phrase into an algebraic expression and then simplify.

$−10$ added to $−15$

Translate each phrase into an algebraic expression and then simplify.

$6$ more than the sum of $−1$ and $−12$

Translate each phrase into an algebraic expression and then simplify.

the sum of $10$ and $−19 ,$ increased by $4$

Solve.

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

Solve.

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

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?

Solve.

Football The Rams took possession of the football on their own $\text{35}-\text{yard line}.$ 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?

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?

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:

$\begin{matrix}\text{Monday} & −504 & \text{Tuesday} & + 142 & \text{Wednesday} & −449 \\ \text{Thursday} & + 410 & \text{Friday} & + 369 & \end{matrix}$

What was the overall change for the week?

Explain why the sum of $−8$ and $2$ is negative, but the sum of $8$ and $−2$ and is positive.