Question

What is the solution set |x-3| >4

Answer 1

`\begin{bmatrix}\mathrm{Solution:}\:&\:x<-1\quad \mathrm{or}\quad \:x>7\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-1\right)\cup \left(7,\:\infty \:\right)\end{bmatrix}`

Explanation:

apply the rule of absolute values: it means that x - 3 < - 4 or x - 3 > 4

solve each one:

x - 3 < -4 , x < -1

x - 3 > 4, x > 7

combine both answer sets