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.

-1 < v < 11

Step-by-step explanation:

(5 - v) < 6

- (5 - v) < 6

5 - v < 6

v > - 1

-5 + v < 6

v < 11

-1 < v < 11

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)