Linear Equations

Simple Equations

100

13=-4k+9

k=-1

200

x/2-7=9

x=32

300

3/5x+22=28

x=10

400

(x+11)/8=-3

x=-35

500

1=(a-13)/-6

a=7

Multi-Step Equations

100

y-3(2y-7)=76

y=-11

200

7(3r-1)-(r+5)=-52

r=-2

300

8(2w-2)=7(3w+2)

w=-6

400

7(p+3)+9=5(p-2)-3p

p=-8

500

3x-13=7(x+2)-4(x-7)

No Solution 

Absolute Value Equations

100

|-6k|=30

k={-5,5}

200

|2k+3|=7

k={-5,2}

300

|(4x-12)/2|=8

x={-1,7}

400

|x+6|=2x

x=6

500

What is the extraneous solution to the equation below?

|4x+10|=6x

x=-1

Literal Equations

100

Solve for r. 

d=2r

r=d/2

200

Solve for d. 

s=(2d)/t

d=(st)/2

300

Solve for m. 

y=mx+b

m=(y-b)/x

400

Solve for 

pi

V=pir^2h

pi=V/(r^2h)

500

Solve for a. 

P=(100a)/t

a=(Pt)/100

Word Problems

100

Ten increased by the quotient of a number and 2 is -15. Find that number. 

x=-50

200

The length of a rectangle is 4x+5 and the width is x. If the perimeter is 90 inches, find its dimensions.

Length: 37 inches 

Width: 8 inches 

300

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. Create an equation for the number of ski trips you would take. 

x=(C-60)/85

400

A common statistic used in professional football is the quarterback rating. This rating is made up of four major factors. One factor is the completion rating given by the formula

R=5(C/A-0.3)

where C is the number of completed passes and A is the number of attempted passes. Create an equation for the number of completed passes. 

C=A(R/5+0.3)

500

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 

7.5 seconds