Answer:
x < -4 ∪ x > 4
Step-by-step 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.
