Solving Equations
Word Problems
Inequalities
Number of Solutions
Slope-Intercept Form
100

Solve for x in the equation below.

5x + 8 = 2x

x = -8/3

100

Write the equation and solve:

The bill for the repair of a computer was $179. The cost for parts was $44, and the labor charge was $45 per hour. How many hours did it take to repair the computer?


44 + 45h = 179

h = 3



100

x + 2 − 2 > 12 − 2

x > 10

100

How many solutions does this equation have?

–6h = –6h − 6

one solution

100

Rod is paid an overtime rate of $25 per hour after his basic wage of $600 per week. Write an equation in slope-intercept form for the total pay p if he works h hour of overtime.

y =25x +600

200

Solve for x in the equation below.

3x - 61 = 2x - 50

x = 11

200

Aliyah had some candy to give to her four children. She first took ten pieces for herself and then evenly divided the rest among her children. Each child received two pieces. With how many pieces did she start?

18

200

−2y < −8

y > 4

200

How many solutions does this equation have?

7x - 3 = 5x + 5


one solution

200

A plumber charges a fee of $50 to make a house call. He also charges $25 an hour for labor. Write an equation that you could use to find the amount a plumber charges for a house call based on the number of hours of labor. Let x represent the number of hours for labor and y represent the total cost.

y = 25x + 50

300

Solve for p in the equation below.

6p+2+ p−3=8p−8

p = 7

300

Write the equation and solve:

The Elk Grove Bowling Alley offers a special. Each game costs $2.50, and shoe rental $2. You spend $14.50 total. How many games did you bowl?


14.50 = 2 + 2.50g

g = 5

300

x−32 ×2 < −5 ×2

𝑥 < 54

300

How many solutions does this equation have?

3(6x + 8) = 24 + 18x

infinitely many solutions

300

The cost of a school banquet is $95 plus $15 for each person attending. Write an equation that gives total cost as a function of the number of people attending. What is the cost for 77 people?


$1,250

400

Solve for v in the equation below.

−22 + 8v = 7 (4v − 6)

v = 1

400


The Cooking Club made some pies to sell at a basketball game to raise money for the new math books. The cafeteria contributed four pies to the sale. Each pie was then cut into five pieces and sold. There were a total of 60 pieces to sell. How many pies did the club make?

8

400

-5x - 6 ≤ (x+17) / -2

𝑥 ≥ 59

400

How many solutions does this equation have?

5x - 8 = 11 - 7x + 12x

no solution

400

Write an equation of the line passing through the point (−7, − 6) with slope m = 4.

y = 4x + 22

500

Solve for n in the equation below.

3n − 2 (−2 −7 n) = 4(1 −8n)

n = 0

500

On Tuesday Shanice bought five hats. On Wednesday half of all the hats that she had were destroyed. On Thursday there were only 17 left. How many did she have on Monday?

29

500

x/3 -6 +6 < 2 + 6 

x < 24

500

How many solutions does this equation have?

-3x + 32 - 7x = -2 (5x + 10)

no solution

500

Pete’s checking account showed a balance at the beginning of the month of $180. After 3 days the checking account showed a balance of $172.50. Write a linear equations to represent the total in the checking account, y, according to the day x.

y = -2.50x + 180

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