Question

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

Answer 1

(-34,∞)∩ (-∞,10)=(-34,10)

Explanation:

its the seaperate compound inequality

Answer 2

The solution of the compound inequality is

(-34,∞)∩ (-∞,10)=(-34,10)

Explanation:

we have

`\left|x+12\right|+5<27`

Subtract 5 both sides

`\left|x+12\right|<27-5`

`\left|x+12\right|<22`

Separate into a compound inequality

`x+12 <22` ------> inequality A

`-(x+12)<22` ------> inequality B

Solve inequality A

`x+12 <22`

`x <22-12`

`x <10`

The solution is the interval (-∞,10)

Solve inequality B

`-(x+12)<22`

Multiply by -1 both sides

`(x+12)>-22`

`x>-22-12`

`x>-34`

The solution is the interval (-34,∞)

therefore

The solution of the compound inequality is

(-34,∞)∩ (-∞,10)=(-34,10)