Multi-Step Equations with Like Terms

Key Questions

• You combine like terms by variable(s) and exponent(s).

The variables and exponent must match in order to combine.

So take ${x}^{2} + x$. Variables (x and x) match, but exponents (2 and 1) do not, so you cannot combine

Take ${x}^{2} + {y}^{2}$. Exponents (2 and 2) match, but variables (x and y) do not.

Now, take $3 {x}^{2} + 5 {x}^{2}$ These CAN be combine since the variable of x and power of 2 match.

So we have $3 {x}^{2} + 5 {x}^{2} = \left(3 + 5\right) {x}^{2} = 8 {x}^{2}$

• Example . Solve: 3x + 4m - 5 = 2x - 2m + 7.
First, combine x terms: -2x = - 2x
x + 4m - 5 = -2m + 7
Next, combine m terms and constants
- 4m + 5 = - 4m + 5
______
x = -6m + 12