Question

Solve and graph the inequality |5 – v| < 6.

Write the inequality as two inequalities without absolute value.

Solve the inequality and write the solution set.

Answer 1

-1 < v < 11

Explanation:

(5 - v) < 6

-(5 - v) < 6

5 - v < 6

v > -1

-5 + v < 6

v < 11

-1 < v < 11

Answer 2

5 - v < 6, 5 - v >= 0

-5 + v < 6, 5 - v < 0

1) - v < 6 -5 (move 5 to the right side and then multiply by -1 both sides of the inequality)
v > -1 (don't forget that here v <= 5)

2) v < 6 + 5 (move -5 to the right side)
v < 11 (here v should be more than 5)

so from 1) you get that v is from -1 to 5 inclusive (-1;5]
and from 2) you get that v is from 5 to 11 (5;11)

so by adding up results from 1) and 2) you get v is (-1; 11)

answer: (-1; 11)