Pre-Algebra: Cross-Multiply to Solve Equations

When an algebraic equation contains fractions, you can use cross-multiplication to solve the equation. The following practice questions contain two equal fractions, where you need to cross-multiply to solve them.

Practice questions

1. Rearrange the equation

   to solve for x.

2. Solve the equation

Answers and explanations

1. x = –4Remove the fraction from the equation by cross-multiplying:

   

   Multiply to remove the parentheses from the left side of the equation:

   8x + 40 = –2x

   At this point, you can solve for x:

   

2. x = 5Remove the fractions from the equation by cross-multiplying:

   

   Remove the parentheses from the left side of the equation by multiplying through by x; remove parentheses from the right side of the equation by FOILing:

   4x² – 7x = 4x² – 10x + 6x – 15

   Rearrange the equation:

   4x² – 7x – 4x² + 10x – 6x = –15

   Notice that the two x² terms cancel each other out: