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Linear Inequalities in One or Two Variables

SAT Math· difficulty 5/5

For what value of kk does ∣2x−k∣≤4|2x - k| \le 4 have solution set [−1,3][-1, 3]?

  • A

    44

  • B

    33

  • C

    11

  • D

    22

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Explanation

The solution set is ((k−4)/2,(k+4)/2)((k - 4)/2, (k + 4)/2) (closed). Setting (k−4)/2=−1(k - 4)/2 = -1 gives k=2k = 2; check (k+4)/2=3(k + 4)/2 = 3 ✓.

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