How do I solve this inequality question?

Question

|x + 7| < 6

Answer 1

|x + 7| < 6

Note: |A| = + A

(x + 7) < 6

Subtract 7 from each side.

x + 7 - 7 < 6 - 7

Simplify

x < - 1

And  - (x + 7) < 6

Note: - (A + B) = - A - B

- x - 7 < 6

Add 7 to each side.

- x - 7 + 7 < 6 + 7

Simplify

- x < 13

 (Multiply each side by negative one and flip the symbol )

x > 13

There fore

x < -1 and x > 13

13 < x < -1

Comments

Solution of the inequality |x+7| < 6 is -13 < x < -1.

Answer 2

The absolute inequality is |x + 7| < 6

|x| < a can be written as - a < x < a

|x + 7| < 6 can be written as -6 < x + 7 < 6

Subtract 7 from each term of inequality.

- 6 - 7 < x + 7 - 7 < 6 - 7

- 13 < x < -1

Solution set is {x Є R| -13 < x < - 1}

Observe the graph , the open circle means that -13 and - 1 are not the solutions of the inequality.