# How to Solve Linear Equations with Both Multiplication and Division

Often, you need to use both multiplication and division to solve a linear equation. When a linear equation uses both multiplication and division, you solve by using the inverse operation of each. So, if a variable is both multiplied and divided by a number in an equation, you solve the equation for that variable by using a combination of multiplication and division.

*Example:*

Apply these steps to solve an equation with multiplication and division by trying to solve for *a*.

Determine the value that divides the variable.

In this case, the 5 is dividing into both the 4 and the variable.

Multiply the values on each side of the equal sign.

Reduce and simplify.

The 5 cancels itself out on the left side of the equation, leaving you with

4

*a*= 12(5)4

*a*= 60Determine what is multiplying the variable.

The number 4 is the coefficient and multiplies the

*a.*Divide the values on each side of the equal sign.

Reduce and simplify.

The 4 cancels itself out on the left side of the equation, leaving you with