Question

Solve the following absolute value inequality graphically: |x|-3>1.

Answer 1

x < -4 ∪ x > 4

Explanation:

The absolute value function is shifted down 3 units. The solution space is values of x where y = |x|-3 is greater than 1. The solution is shown in red in the attachments, and the left and right (dashed) sides of the inequality are shown in blue.

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I personally prefer to rewrite the inequality so the comparison is to zero. That is done in the second attachment, which rewrites it to ...

|x| -4 > 0

by subtracting 1 from both sides. It is often easier to read the values of x-intercepts than it is to read the coordinate values where lines cross each other.