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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 4/5

Solve for xx: xx+3=2x+3+12\dfrac{x}{x + 3} = \dfrac{2}{x + 3} + \dfrac{1}{2}

  • A

    No solution

  • B

    x=7x = 7

    check_circle
  • C

    x=2x = 2

  • D

    x=−3x = -3

Explanation

Multiply by 2(x+3)2(x+3): 2x=4+(x+3)=x+72x = 4 + (x+3) = x + 7, so x=7x = 7. Check: 7/10=2/10+1/2=2/10+5/10=7/107/10 = 2/10 + 1/2 = 2/10 + 5/10 = 7/10 ✓.

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