PSAT Math Multiple-Choice Question 604: Answer and Explanation

Question: 604

If |3x - 1| = 4, what are all of the possible value(s) of x?

I. -1

II.

III. 1

• A. II only
• B. III only
• C. I and II only
• D. All of the above

Correct Answer: C

Explanation:

(C) Recall that absolute value can be thought of as the distance of something from the origin. So if the absolute value of something is 4, it is 4 units away from the origin in either direction. This means that it can be either 4 or -4. Therefore, to solve for the values of x, we can set what's inside the absolute value equal to both 4 and -4 and solve. Setting it equal to 4 gives:

3x - 1 = 4

Adding 1 to both sides results in:

3x = 5

Dividing both sides by 3 gives us our first solution:

Next, set the inside of the absolute value sign equal to -4:

3x - 1 = -4

Adding 1 to both sides gives:

3x = -3

Dividing by 3 gives us our second solution:

x = -1

Therefore, there are two solutions, I and II, choice (C).