Solving Equations
Solve for x in the equation below.
5x + 8 = 2x
x = -8/3
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
x + 2 − 2 > 12 − 2
x > 10
How many solutions does this equation have?
–6h = –6h − 6
one solution
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
Solve for x in the equation below.
3x - 61 = 2x - 50
x = 11
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
−2y < −8
y > 4
How many solutions does this equation have?
7x - 3 = 5x + 5
one solution
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
Solve for p in the equation below.
6p+2+ p−3=8p−8
p = 7
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
x−32 ×2 < −5 ×2
𝑥 < 54
How many solutions does this equation have?
3(6x + 8) = 24 + 18x
infinitely many solutions
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
Solve for v in the equation below.
−22 + 8v = 7 (4v − 6)
v = 1
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
-5x - 6 ≤ (x+17) / -2
𝑥 ≥ 59
How many solutions does this equation have?
5x - 8 = 11 - 7x + 12x
no solution
Write an equation of the line passing through the point (−7, − 6) with slope m = 4.
y = 4x + 22
Solve for n in the equation below.
3n − 2 (−2 −7 n) = 4(1 −8n)
n = 0
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
x/3 -6 +6 < 2 + 6
x < 24
How many solutions does this equation have?
-3x + 32 - 7x = -2 (5x + 10)
no solution
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