Question

| 7 + m | - 4 > 8

Answer 1

Answer:

m > 5 or m < -19

Step-by-step explanation:

We are given the Inequality:

$\displaystyle \large{ |7 + m| - 4 > 8}$

First, add both sides by 4.

$\displaystyle \large{ |7 + m| - 4 + 4 > 8 + 4} \\ \displaystyle \large{ |7 + m| > 12}$

Absolute Value Property

$\displaystyle \large{ |a| = \sqrt{ {a}^{2} } }$

Given a = any expressions and b = any positive numbers, zero or any expressions.

$\displaystyle \large{ |a| = b \longrightarrow a = \pm b}$

From the Inequality, change > to equal

$\displaystyle \large{ 7 + m = \pm12}$

Subtract 7 both sides.

$\displaystyle \large{ 7 - 7 + m = \pm12 - 7} \\ \displaystyle \large{ m = \pm12 - 7}$

±12-7 can be 12-7 = 5 or -12-7 = -19

$\displaystyle \large{ m = 5, - 19}$

Refer to the attachment. The region is when the absolute value function is greater than constant function y = 12 or a blue horizontal line.

Since the absolute graph is above constant graph when x > 5 and x <-19.

Therefore,

$\displaystyle \large{ m > 5, m < - 19}$