Solve. |8x-3| = x+4

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We will have two cases here:
8x - 3 = x + 4 and 8x - 3 = -(x + 4)

Solving for x on 8x - 3 = x + 4:

Subtract both sides by x:

8x - x - 3 = x - x + 4

7x - 3 = 4

Add 3 on both sides.

7x - 3 + 3 = 4 + 3

7x = 7

Divide both sides by 7.

x = 1

Solve for x on the second case.
8x - 3 = -x - 4

Add x on both sides.

8x + x - 3 = -x + x - 4

9x - 3 = -4

Add 3 on both sides.

9x - 3 + 3 = -4 + 3

9x = -1

Divide both sides by -1.

x = -1/9.

Hence, solution set is x = {-1/9, 1}.

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