09.07.2023, solved by verified expert

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Isolate the absolute-value term:

2 |3x - 5| - 4 = 12

2 |3x - 5| = 8

|3x - 5| = 4

Recall the definition of absolute value:

We consider two cases:

• If 3x - 5 ≥ 0, then |3x - 5| = 3x - 5, and the equation resolves to

3x - 5 = 4

3x = 9

x = 3

• Otherwise, if 3x - 5 < 0, then |3x - 5| = -(3x - 5) = -3x + 5, hence

-3x + 5 = 4

-3x = -1

x = 1/3

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