MOSTMATHHome

Chapter 6 · Equations · page 32 of 68

Variables on both sides

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

When the variable shows up on both sides, collect it on one side first by subtracting the smaller variable term from both sides. Then it is a two-step equation.

How to use it

  1. Subtract the variable term from one side so it appears on the other with the opposite sign.
  2. Move the numbers to the other side.
  3. Divide by the coefficient.
  4. Check in both sides of the original.

Example

5x+4=x+16⇒4x+4=16⇒4x=12⇒x=35x + 4 = x + 16 \Rightarrow 4x + 4 = 16 \Rightarrow 4x = 12 \Rightarrow x = 3
2y−7=−3y+13⇒5y=20⇒y=42y - 7 = -3y + 13 \Rightarrow 5y = 20 \Rightarrow y = 4

Where it goes wrong

  • Adding the coefficients instead of subtracting: moving x across 5x gives 4x, not 6x.
  • Moving a term without changing its sign.

Related

Two-step equationsSimplify each side firstCheck by substitution
Practice this