Multiple choice

Solve the equation $\displaystyle\frac { x-5 }{ 7 } =\displaystyle\frac { x+3 }{ 2 } $

  1. $\left\{ -\displaystyle\frac { 31 }{ 5 } \right\} $
  2. $\left\{ -\displaystyle\frac { 11 }{ 5 } \right\} $
  3. $\left\{ \displaystyle\frac { 31 }{ 9 } \right\} $
  4. $\left\{ -\displaystyle\frac { 26 }{ 5 } \right\} $
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A Correct answer
Explanation

Cross-multiply: 2(x - 5) = 7(x + 3). 2x - 10 = 7x + 21. -31 = 5x, so x = -31/5.

AI explanation

Cross-multiply the fractions to get 2(x - 5) = 7(x + 3). Distributing the numbers gives 2x - 10 = 7x + 21. Subtracting 2x and then 21 from both sides yields -31 = 5x. Dividing by 5 gives x = -31/5.

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