How to Solve Linear Equations with Division

A basic method for solving linear equations is to divide each side of the equation by the same number. Many formulas and equations include a coefficient, or multiplier, with the variable. To get rid of the multiplier and solve the equation, you divide.

Example 1: Solve for the value of x in the equation 20x = 170.

  1. Determine the multiplier of the variable and divide both sides by it.

    Because the equation involves multiplying 20x, undo the multiplication in the equation by doing the opposite of multiplication, which is division.

    Divide each side by 20.

    image0.png
  2. Reduce both sides of the equal sign.

    20x ÷ 20 = x

    170 ÷ 20 = 8.5

    x = 8.5

Example 2: You need to buy 300 donuts for a big meeting, but how many dozen donuts is that?

Let d represent the number of dozen donuts you need. There are 12 donuts in a dozen, so 12d = 300. Twelve times the number of donuts you need has to equal 300.

  1. Determine the multiplier of the variable and divide both sides by it.

    Divide each side by 12.

    image1.png
  2. Reduce both sides of the equal sign.

    12d ÷ 12 = d

    300 ÷ 12 = 25

    d = 25 dozen donuts

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