Which inequality describes all the solutions to 5 (3 - x) < - 2x + 6?

A X <-9

B. x > 3

O c. xx-3

D. X>7

Answer: Choice B. x > 3

Work Shown:

5 (3-x) < - 2x+6

15-5x < - 2x+6 ... distribute

15-5x+5x < - 2x+6+5x ... adding 5x to both sides

15 < 3x+6

15-6 < 3x+6-6 ... subtracting 6 from both sides

9 < 3x

3x > 9 ... flip both sides of inequality, flip the inequality sign

3x/3 > 9/3 ... dividing both sides by 3

x > 3

Notice that when going from 3x > 9 to x > 3, the inequality sign does not flip. The sign only flips if you divided both sides by a negative number.