Question

Solve the absolute value inequality: |x + 12| + 5 < 27 Isolate the absolute value by subtracting 5 from both sides.

Answer 1

- 34 < x < 10

Explanation:

Inequalities of the type | x | < a, always have a solution of the form

- a < x < a

given | x + 12 | + 5 < 27 ( subtract 5 from both sides )

| x + 12 | < 22, then

- 22 < x + 12 < 22 ( subtract 12 from all 3 intervals )

- 34 < x < 10

Answer 2

-34 < x < 10

Explanation:

We have to solve absolute value inequality which means that we have to find the value of x.

| x+12 | +5 < 27

Adding -5 to both sides of above inequality,we get

| x+12 | +5-5 < 27-5

| x+12 | +0 < 22

| x+12 | < 22

Since, we know that

| x | < a ⇔ -a< x< a where a is any constant.

hence,

-22 < x+12 < 22

Adding -12 to each side of above inequality,we get

-22-12 < x+12-12 < 22-12

-34 < x+0 < 10

-34 < x < 10 which is solution of given inequality.