Solving Equations Review

Writing and Solving Equations and Inequalities

100

There are an unknown number of apples in a basket. John triples the number of apples. Then he takes out 6 apples. Then he splits the apples into 7 groups. At the end, he has 12 apples. Write an equation for the problem.

Solve for a bonus 100 pts

(3x - 6) / 7 = 12

x = 30

200

John has already climbed 125 steps this week and he can climb 75 steps each day. Find how many days John needs to climb to reach more than 500 steps this week.

Solve for a bonus 100 pts

Represent your solution on a number line: 100 pts

75x + 125 > 500

x > 5

300

Abe needs to reach more than 15000 experience to level up on GameQuest. If Abe already has 10000 xp and he can grind 250 xp every hour, how many more hours does Abe need to play for?

Solve for a bonus 100 pts

Represent your solution on a number line: 100 pts

250x + 10000 > 15000

x > 20

400

Colby's warehouse holds 210 pallets of sportswear. If each week he ships out 4 pallets and he needs to have fewer than 174 pallets to restock, how many weeks until he can restock?

Solve  for a bonus 100pts

Represent your solution on a number line: 100pts

210 - 4x < 174

x > 9

500

William's Welders charge $350 plus $30 per hour of labor to repair the frame of an industrial apple slicer. Max's Mechanics charge $200 plus $45 per hour labor for the same service. After how many hours of labor will William's Welders be cheaper?

Solve for a bonus 100 pts

Represent your solution on a number line: 100 pts

350+30x < 200 + 45x

x > 10

Solving Equations with Variables

100

A = L * W

Solve for W

W = A / L

200

Rewrite the following in slope intercept form(y=mx+b):

6x + 2y = 10

y=(10 - 6x) / 2

or

y=5 - 3x

300

(ax+b)/c = d

Solve for x

(dc - b) / c

400

(2/3)x - 9y = z

Solve for x

x = (z + 9y) / (2/3)

or

x = (3/2)z + (27/2)y

500

x² / (a - b) = c

Solve for x

x = (c(a - b))^1/2

Two-Step Equations

100

6x – 13 = 11

x= 4

200

3x + 5 = 14

x= 3

300

(x/2) +10=-8

x= -36

WILD CARD - BONUS 100 POINTS - IF CORRECT

400

(x/2)-4=10

x= 28

500

(x/3)+12=-3

x= -45

Multi-Step Equations

100

Solving Equations

4x + 3 = 7

x = 1

200

Solving Equations

4(6 + 5x) = 124

x = 5

300

Solving Equations

-108 = -8(x + 6) - 4

x = 7

400

Solving Equations

172 = 5(4a + 6) + 2

a=7

500

Solving Equations

-93 = 7(-3k - 8) + 5

k = 2

Multi-Step Equations w/ Variables on Both Sides

100

Solving Equations

5n - 2 = 8n - 14

n = 4

200

Solving Equations

-4(-8p + 1) = -4 - 8p

p = 0

300

Solving Equations

6(6n - 2) = 8n - 40

n = -1

400

Solving Equations

5x + 5 + 4x = 4 - 3x + 6

x= 5/12    or    x= 0.41667

WILD CARD - BONUS 100 POINTS - IF CORRECT

500

What is the general process for solving equations if you know the order of operations that apply to x? (2 important pieces)

Do the opposite in reverse order