Answer:
D: {1/2, 4 1/2} or {0.5, 4.5}
Step-by-step explanation:
Start by simplifying this equation. Divding both sides by 3, we get:
|2x - 5| = 4
Now divide all terms by 2 to isolate x inside the absolute value signs:
|x - 5/2| = 2
We regard 5/2 as the center; the two solutions are 2 units distant from this center on either side:
Case 1: x = 5/2 + 2, or x = 9/2, or x = 4.5
Case 2: x = 5/2 - 2, or x = 1/2, or x = 0.5
Check: is 9/2 two units to the right of the 'center' 5/2? Is 5/2 + 2 = 9/2? YES
Is 12 two units to the left of the 'center' 5/2? Is 5/2 - 4/2 = 1/2? YES
The solution set is D: {1/2, 4 1/2} or {0.5, 4.5}
