Solve |3x - 4| = 15 a. {-19/3, 19/3} b. {11/3, 19/3} c. {-11/3, 19/3}

First, we need to split this into two problems. One problem where the absolute value is positive, and one where the absolute value is negative.

1. + (3X-4) = 15

2. - (3X-4) = 15

Now we need to solve. Let's solve "1" first

3X-4=15

First, we need to get 3X by itself. We do this by adding four to both sides.

3X-4+4=15+4

3X=19

Now we divide both sides by 3.

3X/3=19/3

X=19/3

Now we have one of our answers. However, all of the choices have 19/3 as part of the answer, so we cannot eliminate any choices.

Next we solve our second problem.

- (3X-4) = 15

We must first get rid of the parentheses. Because the negative sign distributes, we must change the signs of 3X and - 4.

- (3X-4) = 15

-3X+4=15

Now we need to get - 3X by itself. We do this by subtracting 4 from both sides.

-3X+4-4=15-4

-3X=11

Now we need to divide both sides by - 3.

(-3X) / (-3) = 11 / (-3)

X=11 / (-3)

The negative sign on the bottom affects the whole right side, so we can move the negative to the front.

X=11 / (-3)

X=-11/3

Now that we have the second answer, we can say that the answer is "c."