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

Answer:

The solution of the compound inequality is

(-34,∞)∩ (-∞,10)=(-34,10)

Step-by-step explanation:

we have

$\left|x+12\right|+5$

Subtract 5 both sides

$\left|x+12\right|$

$\left|x+12\right|$

Separate into a compound inequality

$x+12$ ------> inequality A

$-(x+12)$ ------> inequality B

Solve inequality A

$x+12$

$x$

$x$

The solution is the interval (-∞,10)

Solve inequality B

$-(x+12)$

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)

Answer 2

Answer:

(-34,∞)∩ (-∞,10)=(-34,10)

Step-by-step explanation:

its the seaperate compound inequality