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Linear Equations in One Variable

SAT Math· difficulty 5/5

The equation x+a2−x−a3=5\frac{x + a}{2} - \frac{x - a}{3} = 5 has solution x=6x = 6. What is the value of aa?

  • A

    3

  • B

    125\frac{12}{5}

  • C

    245\frac{24}{5}

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  • D

    6

Explanation

Multiply by 6: 3(x+a)−2(x−a)=303(x + a) - 2(x - a) = 30, so x+5a=30x + 5a = 30. With x=6x = 6: 5a=245a = 24 and a=245a = \frac{24}{5}.

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