PSAT Math Multiple-Choice Question 625: Answer and Explanation

Question: 625

If -2| -3| < -3|x + 5|, what are all possible values of x?

• A. -7 < x < -3
• B. -3 < x OR -7 > x
• C. -3 < x
• D. No solutions

Correct Answer: A

Explanation:

(A) Let's start with the left side of the inequality. The absolute value of -3 is 3, so:

-2|-3| = -2(3) = -6

-6 < -3|x + 5|

We want to isolate our absolute value. So let's divide by -3, flipping the inequality since we are dividing by a negative number:

2 > |x + 5|

Because 2 has to be greater than the absolute value, the expression inside of the absolute value symbol can be anything between (-2, 2). In other words, x - 5 needs to be greater than -2 but less than 2. To find the x-values such that x - 5 is less than 2, simply take away the absolute value signs and solve for x:

2 > x + 5

Subtracting 5 from both sides gives:

-3 > x

Next, we want to find the values of x such that x - 5 is greater than -2. In other words, we want to solve for x in the inequality -2 < x + 5. Subtracting 5 tells us:

-7 < x

We have found that -3 > x and that -7 < x. In other words, -7 < x < -3, which is choice (A).