Solutions of Equations

Which equation has no solution?

• 3x + 7 = 7

• 7 + 3x = 3x - 7

• 15 + x = x + 15

• -2x + 5 = 5x - 2

How many solutions does the equation

10 - 3x + 10x - 7=5x - 5 + 2x + 8 have?

• one solution

• two solutions

• no solution

• infinitely many solutions

Solve for x:

1/7x - 6 = 3/7x + 4

• 30

• -35

• 42

• -40

When you solve 4(x + 2) = 22, you must simplify the equation first. What would the first step look like?

• 4x + 8 = 22

• 4x + 2 = 22

• x + 8 = 22

• x + 2 = 22

Solve for x:

5(x - 8) = 3x + 4

• 1.5

• 6

• 11

• 22

Solve:

-5x + 10 = -2x - 11

• 6

• 7

• -6

• -7

Solve for x:

2(2x + 6) = 8x - 28

• x=9

• x=2

• x=10

• x=6

One way to solve this equation

2/7 x + 3 = 8/7 x - 8

is to first

• multiply both sides through by 2

• multiply both sides through by 8

• multiply both sides through by 7

• add x to both sides

If you double a number and then add 12, you get 4/5 of the original number. Let x represent the original number.

Which equation represents this situation?

• 2x + 4/5 = 12

• 2x + 12 = 4/5 x

• 4/5 + 4x = 5

• 12x - 2 = 4/5 x

Carpet Cleaner A charges $28.95 plus $18 per room. Carpet Cleaner B charges $19.85 plus $32 per room. Which equation can be used to find the number of rooms for which the total cost of both carpet cleaners is the same?

• 28.95x + 18 = 19.85 + 32

• 28.95 + 32x = 19.85 + 18x

• 28.95 + 18x = 19.85 + 32x

• (28.95 + 18)x = (19.85 + 32) x