Calculate the absolute value
| 4 - 3x | = 5x + 4

Recall the definition of absolute value:

• |x| = x if x ≥ 0

• |x| = -x if x < 0

So we have 2 cases to consider:

• If 4 - 3x ≥ 0, then |4 - 3x| = 4 - 3x, and we have

4 - 3x = 5x + 4

8x = 0

x = 0

• If 4 - 3x < 0, then |4 - 3x| = -(4 - 3x) = 3x - 4, which gives

3x - 4 = 5x + 4

2x = -8

x = -4

However, keep in mind that |x| is always non-negative. If x = -4, then the right side of the equation becomes

5(-4) + 4 = -20 + 4 = -16 < 0

so the solution in this case is extraneous.

domain is all the x values included in the

0 ≤ x ≤ 2

range is all the y values of the graph

-2 ≤ y ≤ 2

***keep in mind that there are different ways to show domain and range

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the answer is c

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