Pre-Algebra Practice Questions: Cross-Multiply to Solve Equations

By Mark Zegarelli

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

    PREALGEBRA_3301

    to solve for x.

  2. Solve the equation

    PREALGEBRA_3302

Answers and explanations

  1. x = –4

    Remove the fraction from the equation by cross-multiplying:

    PREALGEBRA_3303

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

    8x + 40 = –2x

    At this point, you can solve for x:

    PREALGEBRA_3304

  2. x = 5

    Remove the fractions from the equation by cross-multiplying:

    PREALGEBRA_3305

    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:

    PREALGEBRA_3306