Integer & Algebra Review

Integers Operations

100

−8+(−6)−5

-19

200

−15−(−4)+9

-2

300

6+(−4)×(−3) 

18

400

(−36)÷6+(−5)

-11

500

−18+4×(−6)÷3

-26

Integer Word Problems

100

The temperature is −3⁰ C in the morning. By noon, it rises 7 degrees. What is the new temperature?

−3+7=4⁰ C

200

A submarine is 15 m below sea level. It rises 9 m. What is its new position relative to sea level?

−15+9=−6 m

300

A hockey team loses 4 points in each of 6 games. What is the total change in points?

−4×6=−24

400

The temperature drops 4 degrees every hour for 5 hours, starting at 6⁰ C.
What is the final temperature?

Drop per hour: −4
Total drop: −4×5=−20-
6+(−20)=−14⁰ C

500

A hiker starts at an elevation of 120 m above sea level. They descend 35 m, then climb 18 m, and finally descend 60 m. What is the hiker’s final elevation relative to sea level?

Start: +120+120+120 m. Descend 35 m → 120−35=85. Climb 18 m → 85+18=103. Descend 60 m → 103−60=43. 

The hiker ends 43 m above sea level.

Solve the inequality

100

x + 4 > 9

x > 5

200

3x ≤ 12

x ≤ 4

300

2x - 5 ≥ 9

x ≥ 7

400

-4x < 20

x > -5

500

A movie ticket costs $8. You have at most $40 to spend. Write and solve an inequality to find the maximum number of tickets you can buy.

8x ≤ 40

x ≤ 5

Solving Algebraic Equations

100

x+3 when x = 8

11

200

2x+ 5 when x = 10

25

300

3x+1 - (-2) when x = (-3)

-6

400

4(x−2)+ 6 - (1 + 3x) when x = 3

0

500

Which value of x makes the statement true: 3(x−1)=6? Does x=2 or does x=5

Trick question! Neither value makes the statement true. Correct value would be x=3

Simplifying, Expanding & Factoring Expressions

100

Simplify: 5x+3x

5x+3x=8x

200

Simplify: 7y−2y+4

7y−2y+4=5y+4

300

Expand: 3(x+4)

3(x+4)=3x+12

400

Expand and simplify: 2x+3(x−5)

2x+3(x−5)
=2x+3x−15
=5x−15

500

Factor completely:6x+12

6x+12=6(x+2)