SAT Practice Math Questions: Absolute Value

By Geraldine Woods, Ron Woldoff

Absolute value presents you with a number, letter, or expression inside of two lines. So what you do when one pops up in an equation on the SAT Math test? The following practice problems should point the way.

Practice questions

  1. In the equation |x – 4| = 3, x could equal
    • A. 7 only
    • B. 1 only
    • C. 7 or 1
    • D. 7 or –1
  2. The solution set to the equation |x + 3| = 5 is
    • A. {2}
    • B. {2, –8}
    • C. {–8}
    • D. {–2, –8}

Answers and explanations

  1. C. Because an absolute value symbol turns everything into a positive number, the expression inside the absolute value could equal either 3 or –3. This is the key to solving an equation with an absolute value. If |something| = n, then either something = n or something = –n. You must solve each of these equations separately to get two answers. But there’s a catch: You also must check each answer in the original equation. Only solutions that make the original equation true count in your final answer.
    1401

    Check your work:
    1402

    Because both checks work, your answer is Choice (C): 7 or 1. The value of x can’t be both 7 and 1. x has one value, and that’s why the problem says, “x could equal.”

  2. B. You could just plug in all the choices, but, for practice, go through the official steps. First, create two equations:

x + 3 = 5 and x + 3 = –5

Solve them separately:

1403

Check your answers:

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So the answers that work are 2 and –8. Choice (B) is correct.