Linear Equations

How Many Solutions?

100

5x + 2 = 2x + 14

One Solution

200

10x + 12 = 2(5x + 6)

Infinitely Many Solutions

300

4x + 10 + x = 2.5(2x - 4)

No Solution

400

-1/2(24 + 6x) = -3(x - 4)

No Solution

500

1.5(2x - 4) - 1.5x + 3

One Solution

Writing Equations

100

The product of a number and 6 is 3 more than 5 times the number.

6x = 3 + 5x

200

The quotient of 5 times a number and 7 is equal to 10.

28 + 8x

300

Two more than a certain number is 15 less than the product of 7/8 and the number.

x + 2 = 7/8x - 15

400

Two more than 16 times a number is the same as 21 less than the product of -7 and the number.

16x + 2 = -7x - 21

500

Decreasing -5 times a number by 18 is equal to decreasing 9 times the number by 25.

-5x - 18 = 9x - 25

Two Step Equations

100

2x + 4 = 14

x=5

200

-9x + 1 = -80

9

300

2+ x/4 = -2

-16

400

x/2 - 10 = -6

8

500

9x - 7 = -7

0

Multistep Equations

100

8x + 13x = 42

2

200

10(1 + 3x) = -20

-1

300

4(-x + 4) = 12

1

400

-6(1 - 5x) = 54

2

500

8= 8x - 4(x + 8)

10

Variables on Both Sides

100

8x - 2 = -9 + 7x

-7

200

p - 1 = 5p + 3p - 8

1

300

3n - 5 = -8(6 + 5n)

-1

400

2(4x - 3) - 8 = 4 + 2x

3

500

-5(1 - 5x) + 5(-8x - 2) = -4x - 8x

-5