1. 1.3 Solving Equations with Variables on Both Sides

2. Example 1
Get all variables on the same side by using the addition/subtraction property of equality
2x – 2 = -3x + 3
+3x x
5x – 2 = 3
5x = 5
x = 1

3. Example 2 6m + 5 -7m = 10 - 5m + 3 -m + 5 = -5m + 13 + 5m + 5m
4m = 8
m = 2

4. You try!
-2x = 3x + 10
-3x -3x
-5x = 10
x = -2

5. Example 3

6. You Try!

7. Core Concept Special Solutions to Linear Equations
- Identity: an equation that is true for all values of the variable. An Identity has infinitely many solutions.

8. You Try!
3(5x+2) = 15x
-2(4y + 1) = -8y - 2

9. Distance upstream = Distance downstream
Example 4
A boat leaves New Orleans and travels upstream on the Mississippi River for 4 hours. The return trip only takes 2.8 hours because the boat travels 3 miles per hour faster downstream because of the current. How far does the boat travel upstream?
HINT:
Distance = rate x time
Distance upstream = Distance downstream

10. You try!
Write and solve an equation to determine in how many months you would pay the same total amount for each internet service.
Installation fee
Price per month
Company A
$60.00
$42.95
Company B
$25.00
$49.95