Answer:
m > 5 or m < -19
Step-by-step explanation:
We are given the Inequality:
[tex] \displaystyle \large{ |7 + m| - 4 > 8}[/tex]
First, add both sides by 4.
[tex] \displaystyle \large{ |7 + m| - 4 + 4 > 8 + 4} \\ \displaystyle \large{ |7 + m| > 12}[/tex]
Absolute Value Property
[tex] \displaystyle \large{ |a| = \sqrt{ {a}^{2} } }[/tex]
Given a = any expressions and b = any positive numbers, zero or any expressions.
[tex] \displaystyle \large{ |a| = b \longrightarrow a = \pm b}[/tex]
From the Inequality, change > to equal
[tex]\displaystyle \large{ 7 + m = \pm12}[/tex]
Subtract 7 both sides.
[tex]\displaystyle \large{ 7 - 7 + m = \pm12 - 7} \\ \displaystyle \large{ m = \pm12 - 7}[/tex]
±12-7 can be 12-7 = 5 or -12-7 = -19
[tex] \displaystyle \large{ m = 5, - 19}[/tex]
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,
[tex] \displaystyle \large{ m > 5, m < - 19}[/tex]
