Solving Equations

Multi-Step Equations

100

Solve the equation for x:

2x+5=15

x=5

200

Solve the equation for x:

3x-4=2x+5

x=9

300

Solve the equation for x:

4(x-2)+6=18

x=5

400

Solve the equation for x:

5x+2(x-1)=3x+10

x=3

500

Solve the equation for x:

-3(2x+6)=6(3x+1)

x=-1

Clearing Fractions

100

Solve the equation for x:

x/2+1=-1/2

x=-3

200

Solve the equation for x:

(3x)/4-2=4

x=8

300

Solve for x:

(2x-5)/3=(x-1)/2

x=13

400

Solve for x:

(5x+2)/6-x/3=4

x=11/2 or 5.5

500

Solve for x:

(2x+6)/4=(x+3)/2

Infinite solutions (All real numbers)

Literal Equations

100

Solve for x:

y=3x+7

x=(y-7)/3

200

Solve for h:

A=1/2bh

h=2A/b

300

Solve for w: 

P=2l+2w

w=(P-2l)/2

400

Solve for c²

E=mc²

c^2=E/m

500

Solve for m:

y-5=m(x-2)

m=(y-5)/(x-2)

Applications

100

If the length of a rectangle is 4x+3 inches and its width is 3x-2 inches and its perimeter is 184 inches, what is x?

x=13

200

A rock is thrown vertically up in the air. The height, h, in feet of the rock after t seconds can be found using the following equation. Find the height of the rock after 2 seconds.

h=-16t^2+128t

h=192 feet

300

The sum of two numbers is 45. One number is 9 more than the other. Write an equation to find the numbers.

x+(x+9)=45

The numbers are 18 and 27.

400

The perimeter of a rectangle is 56 cm. The length is 3 times the width. Write an equation and find the dimensions.

The width is 7 cm and the length is 21 cm

500

A train travels 60 mph. How long will it take the train to travel 150 miles? Use the equation below. Give your answer in minutes.

d=rt

24 minutes