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Linear Equations in One Variable

SAT Math· difficulty 3/5

Which value of xx satisfies ∣3x+1∣=2x+6|3x + 1| = 2x + 6?

  • A

    55

  • B

    −75-\dfrac{7}{5}

  • C

    Both A and B

    check_circle
  • D

    11

Explanation

Case 1: 3x+1=2x+6⇒x=53x + 1 = 2x + 6 \Rightarrow x = 5. Check ∣16∣=16|16| = 16 ✓. Case 2: 3x+1=−(2x+6)⇒5x=−7⇒x=−7/53x + 1 = -(2x + 6) \Rightarrow 5x = -7 \Rightarrow x = -7/5. Check: ∣3(−7/5)+1∣=16/5|3(-7/5) + 1| = 16/5 and 2(−7/5)+6=16/52(-7/5) + 6 = 16/5 ✓.

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