Solving Equations

One-Step Equations

1

4 = -8 + x

x= 12

2

(x/2) =-8

x= -16

3

3 = -2 – x

x= -5

4

5x = -80

x= 16

5

(x/2)=10

x= 20

Two-Step Equations

1

6x – 13 = 11

x= 4

2

3x + 5 = 14

x= 3

3

-10x + 4 = 74

x = -7

4

x / 2 - 4 = 0

x = 8

5

2x - 7 = 21

x = 14

Multi-Step Equations

1

Solving Equations

x + 3 + 3x = 7

x = 1

2

Solving Equations

5 + 5x - 1 = 29

x = 5

3

Solving Equations

18 = 2(x + 4)

x = 5

4

Solving Equations

14 = 2a + 6 + 2

a= 3

5

Solving Equations

-21 = 7(5k - 8)

k = 1

Equations with Variables on Both Sides

1

4x - 2 = 3x + 5

x = 7

2

2x - 8 = 5x + 4

x = -4

3

4x + 3 = 2x + 11

x = 4

4

9 - x = 6 + 2x

x = 1

5

10x - 15 = 9x - 15

x = 0

Word problems

1

John makes $12.50/hour gardening. He earned $275 this week. Write the equation for figuring out his hours worked

12.5x = 275

x = 22 hours

2

A father is buying cheeseburgers for his children. Each cheeseburger costs $3.50. He spends $17.50 on cheeseburgers. How many cheeseburgers did he buy? 

What is the equation for the number of cheeseburgers he bought.

3.50x = 17.50

x = 5

3

A plant is 14 inches tall. If it grows 3 inches per year, how many years will it take to reach a height of 38 inches? 

What is the equation for the number of years it will take to grow?

14 + 3x = 38

x = 8 years

4

Ryan has one less than four times the number of songs on his iPod that Olivia has. In total, they have 469 songs. How many songs does Olivia have? 

What is the equation used to solve for the number of songs Olivia has?

n + 4n-1 = 469

n = 114

5

The sum of two consecutive integers is 113. Find the integers. 

Find the equation used to find the integers.

x + x + 1 = 113

x = 56, 57 is the next number