Solving Simple Equations
-n/5 = -3
n = 15
2.5x − 13 = 2
x = 6
5x − 4 = 3x + 12
x = 8
∣3x + 9 ∣ − 10 = −4
x = -1 and x = -5
C = 5/9 (F − 32). Solve for f
f= 9/5c+32
200 = 19.32r
r= 10.35
−4(2m + 5) − 3m = 35
m = -5
3(3x − 4) =1/4 (32x + 56).
x = 26
4 ∣2x + 7 ∣ = 16
x = -5.5 and x = -1.5
a = bx + cx + d. Solve for x
x= a-d/b+c
n-6=-7
n = -1
2x(5 − 3) − 3x = 5
x = 5
−3 —4 (8n + 12) = 3(n − 3)
n = 0
∣4x − 10 ∣ = 2 ∣3x + 1 ∣
x= -6 and x = 0.8
The total cost C (in dollars) to participate in a ski club is given by the literal equation C = 85x + 60, where x is the number of ski trips you take. Solve for x
x = c-60 / 85
The temperature at 5 p.m. is 20°F. The temperature at 10 p.m. is −5°F. How many degrees did the temperature fall?
25 degrees F
During the summer, you work 30 hours per week at a gas station and earn $8.75 per hour. You also work as a landscaper for $11 per hour and can work as many hours as you want. You want to earn a total of $400 per week. How many hours must you work as a landscaper?
12.5 h
You and your friend drive toward each other. The equation 50h = 190 − 45h represents the number h of hours until you and your friend meet. When will you meet?
2 hours
∣x − 1 ∣ + 5 = 2
no solution
How many ski trips do you take if you spend a total of $315? $485?
x = c-60/85
3 trips and 5 trips
The balance of an investment account is $308 more than the balance 4 years ago. The current balance of the account is $4708. What was the balance 4 years ago?
$4400
A repair bill for your car is $553. The parts cost $265. The labor cost is $48 per hour. Write and solve an equation to fi nd the number of hours of labor spent repairing the car
6 hours
A cheetah that is running 90 feet per second is 120 feet behind an antelope that is running 60 feet per second. How long will it take the cheetah to catch up to the antelope?
4 seconds
Starting from 300 feet away, a car drives toward you. It then passes by you at a speed of 48 feet per second. The distance d (in feet) of the car from you after t seconds is given by the equation d = ∣300 − 48t ∣ . At what times is the car 60 feet from you?
5 seconds and 7.5 seconds
The penny size of a nail indicates the length of the nail. The penny size d is given by the literal equation d = 4n − 2, where n is the length (in inches) of the nail.
a. Solve the equation for n.
b. Use the equation from part (a) to fi nd the lengths of nails with the following penny sizes: 3, 6, and 10.
a. n =d + 2 / 4
b. 1 1 — 4 in.; 2 in.; 3 in
The recommended weight of a soccer ball is 430 grams. The actual weight is allowed to vary by up to 20 grams.
a. Write and solve an absolute value equation to fi nd the minimum and maximum acceptable soccer ball weights.
b. A soccer ball weighs 423 grams. Due to wear and tear, the weight of the ball decreases by 16 grams. Is the weight acceptable?
a. ∣x − 430 ∣ = 20; 410 g, 450 g
b. no; 407 grams is below the minimum acceptable weight.