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Linear Equations in One Variable

SAT Math· difficulty 4/5

What is the sum of all values of xx that satisfy ∣2x−5∣=∣x+1∣|2x - 5| = |x + 1|?

  • A

    223\frac{22}{3}

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  • B

    6

  • C

    203\frac{20}{3}

  • D

    43\frac{4}{3}

Explanation

Case 1: 2x−5=x+12x - 5 = x + 1, so x=6x = 6. Case 2: 2x−5=−(x+1)2x - 5 = -(x + 1), so 3x=43x = 4 and x=43x = \frac{4}{3}. Sum =6+43=223= 6 + \frac{4}{3} = \frac{22}{3}.

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