1. 3-3: Equations with Variables on Both Sides
Essential Question: How is solving an equation with variables on both sides of an equal sign different than solving an equation with variables on the same side of an equal sign?
3-3: Equations with Variables on Both Sides

2. 3-3: Equations with variables on both sides
To solve an equation that has variables on both sides, use addition or subtraction properties to get all variables to one side of the equation.
Example 1: Variables on both sides
Solve: 6x + 3 = 8x – 21
6x + 3 = 8x – x x
-2x + 3 =
-2x = -24 ÷-2 ÷-2
x = 12

3. 3-3: Equations with variables on both sides
Your Turn
Solve each equation
-6d = d + 4
d = -4/7
2(c – 6) = 9c + 2
c = -2
m – 5 = 3m
m = -5/2
7k – 4 = 5k + 16
k = 10

4. 3-3: Equations with variables on both sides
Example 2: Real-World Problem Solving
Renting in-line skates and safety equipment costs $3.50 an hour, and renting only safety equipment costs $1.50/hour.
You can buy used in-line skates from your friend for $40, or you can rent some.
Either way, you must rent safety equipment. How many hours must you skate for the cost of renting and buying skates to be the same?
h = 3.5h h h
40 = 2h ÷2 ÷2
20 = h

5. 3-3: Equations with variables on both sides
Your Turn
A hairdresser is considering ordering a certain shampoo. Company A charges $4 per 8-oz bottle plus $10 shipping per order. Company B charges $3 per 8-oz bottle plus $25 shipping per order. How many bottles must the hairdresser buy to justify using company B?
15 bottles

6. 3-3: Equations with variables on both sides
If all variables get eliminated and…
The remaining statement is true, it is an identity.
The remaining statement is false, the equation has no solution.
Example 4
10 – 8a = 2(5 – 4a) 6m – 5 = 7m + 7 – m
10 – 8a = 10 – 8a 6m – 5 = 6m a a m m
10 = = 7
Identity No Solution

7. 3-3: Equations with variables on both sides
Your Turn
Determine whether each equation is an identity or whether it has no solution.
9 + 5n = 5n – 1
No solution
9 + 5x = 7x + 9 – 2x
Identity

8. 3-3: Equations with variables on both sides
Assignment
Practice 3-3
1 – 35, odd problems
Quiz tomorrow on 3-1 & 3-2