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Linear Inequalities in One or Two Variables

SAT Math· difficulty 4/5

Which is equivalent to 5−∣x−2∣≥15 - |x - 2| \ge 1?

  • A

    −2≤x≤6-2 \le x \le 6

  • B

    ∣x−2∣≥4|x - 2| \ge 4

  • C

    Both B and C

    check_circle
  • D

    ∣x−2∣≤4|x - 2| \le 4

Explanation

−∣x−2∣≥−4⇒∣x−2∣≤4-|x - 2| \ge -4 \Rightarrow |x - 2| \le 4, i.e., −4≤x−2≤4⇒−2≤x≤6-4 \le x - 2 \le 4 \Rightarrow -2 \le x \le 6.

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