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show how to solve absolute value equations

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you have an extra (-) there, so i assume you mean |4x+5| - 7 = 0

first step is to solve for the absolute expression...

|4x+5| = 7

now that we have this, imagine what this would mean: |y|=7

this means either y=7 or y=-7  (same as -y=7)

we use this same idea...

4x+5 = 7  or  4x+5 = -7

solving the first one, we get 4x=2 which leads to x = 1/2

and the second one gets us 4x=-12 which leads to x = -3