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Chapter 9 · Questions · page 63 of 68

How do you solve an equation with variables on both sides?

Short answerSubtract one of the variable terms from both sides so the variable is on one side only, then solve the two-step equation that is left. 7x + 2 = 3x + 18 becomes 4x + 2 = 18, so x = 4.

levelAlgebra 1
standard8.EE.C.7b
practiceMulti-step equations

You cannot solve while x is on both sides, so the first job is to gather it. Subtracting the smaller variable term usually keeps the coefficient positive, which means fewer sign slips.

How to use it

  1. Subtract the variable term from one side, on both sides.
  2. Move the numbers to the other side.
  3. Divide by the coefficient.
  4. Check in both sides of the original.

Example

7x+2=3x+18⇒4x+2=18⇒4x=16⇒x=47x + 2 = 3x + 18 \Rightarrow 4x + 2 = 18 \Rightarrow 4x = 16 \Rightarrow x = 4
5n−9=2n+6⇒3n=15⇒n=55n - 9 = 2n + 6 \Rightarrow 3n = 15 \Rightarrow n = 5

Where it goes wrong

  • Adding the variable terms instead of subtracting: 7x and 3x give 4x, not 10x.
  • Moving a term without changing its sign.

Related

Variables on both sidesSimplify each side first
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