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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:

image0.png

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

  1. Determine the value that divides the variable.

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

  2. Multiply the values on each side of the equal sign.

    image1.png
  3. Reduce and simplify.

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

    4a = 12(5)

    4a = 60

  4. Determine what is multiplying the variable.

    The number 4 is the coefficient and multiplies the a.

  5. Divide the values on each side of the equal sign.

    image2.png
  6. Reduce and simplify.

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

    image3.png
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