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Linear Equations in One Variable

SAT Math· difficulty 5/5

For what values of cc does ∣x−3∣<c|x - 3| < c describe an interval entirely within (0,6)(0, 6)?

  • A

    c≤6c \le 6

  • B

    0<c≤30 < c \le 3

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  • C

    c<3c < 3

  • D

    c≤3c \le 3

Explanation

Solution is (3−c,3+c)(3 - c, 3 + c). Need 3−c≥03 - c \ge 0 and 3+c≤63 + c \le 6, i.e., c≤3c \le 3, and c>0c > 0 for nonempty interval.

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