How to Solve Linear Equations with Multiplication

To solve linear equations with multiplication, you first determine that division is being used in the linear equation. Multiplication is the inverse (opposite) operation of division, so you can use multiplication to solve equations where you notice that a number divides the variable.

Example: Solve for y by using multiplication.


  1. Determine the value that divides the variable and multiply both sides by it.

    In this case, 11 is dividing into the y, so that’s what you multiply by.


  2. Reduce both sides of the equal sign.

    Because the number 11 on the left side of equation cancels itself out, you only need to multiply the right side of the equation, resulting in:

    y = –22