Digital PSAT Math Practice Question 51: Answer and Explanation

Question: 51

What is the value of x in the following equation?

• A. 1
• B. -1
• C. 3
• D.

Correct Answer: B

Explanation:

(B) To add all of these fractions, you need a common denominator. The least common denominator for the three fractions is 16. However, because the other side has a denominator of 32, let's use 32 for ease. To convert to a fraction with a denominator of 32, multiply both the numerator and the denominator by 4. Thus, becomes . Similarly, becomes after multiplying both the numerator and denominator by 2. Finally, becomes after multiplying both the numerator and denominator by 16. Therefore, we're left with:

Combining like terms gives:

To isolate x, divide both sides by . Dividing by a fraction is the same as multiplying by its reciprocal, so you're left with:

So x = -1, or choice (B).