1. 1.3 Solving Equations with Variables on Both Sides

2. Goal:
Get the variables to one side of the equation and the constants to the other side using APE or SPE

4. Example :

5. Steps to solve multi-step linear equations
If there are ( ) distribute
Collect like terms on same side.
Move variables to same side of equation. (APE or SPE)
Move the constant to the other side of the equation (APE or SPE)
Solve for x using the (MPE or DPE)

6. Example : 6m +5 – 2m = 10 – 3m +16 4m +5 = 26 – 3m +3m 7m +5 = 26 -5

7. 3(n - 2) – 1 = 2 – 5(n + 5) 3n - 6 – 1 = 2 – 5(n + 5)
Ex 4:
3n - 6 – 1 = 2 – 5(n + 5)
3n - 6 – 1 = 2 – 5n - 25
3n = -23 – 5n
5n +
+5n
8n = -23 +7 +7
8n = -16
n =-2

8. No Solution VS. Infinitely Many Solutions
Variable cancels out
Left with a false equation
Variable cancels out
Left with a true equation

12. Assignment: TB: Page 22 (6-24) even