1. Lesson 12: more on Equations

2. What happens when there are 2 variables in an equation?
Multiple variables
What happens when there are 2 variables in an equation?
Combine (simplify) (clean algebra) and solve!

3. 3𝑎+2=12−2𝑎 + 2𝑎 + 2𝑎 5𝑎 + 2 = 12 − 2 − 2 𝑎 = 2 5𝑎 = 10 5 5 Example 1
Move all the variables to one side, and everything else to the other side!
+ 2𝑎
+ 2𝑎 5𝑎
+ 2 = 12
− 2
− 2 𝑎 = 2 5𝑎 = 10 5 5

4. Check! 𝑎 = 2
3𝑎+2=12−2𝑎
3(2)+2=12−2(2)
6+2
=12−4 8
= 8

5. Example 2
2𝑏−5=4𝑏 −2
−4𝑏
−4𝑏
−2𝑏 −5 = −2
− 3 2 +5 +5 𝑏 =
−2𝑏 = 3 −2 −2

6. 𝑏 = 2𝑏−5=4𝑏 −2 2(− 3 2 )−5=4(− 3 2 )−2 − 6 2 −5 =− 12 2 −2 Check!

7. Check!
− 6 2 −5
=− 12 2 −2
− 6 2 − 10 2
=− 12 2 − 4 2
− 16 2
=− 16 2

8. 3 𝑐+1 =8−𝑐 3𝑐 + 3 = 8−𝑐 + 𝑐 + 𝑐 𝑐 = 4𝑐 + 3 = 8 − 3 − 3 = 4𝑐 5 4 4
Example 3
3 𝑐+1 =8−𝑐 3𝑐
+ 3 =
8−𝑐
+ 𝑐
+ 𝑐
5 4 𝑐 = 4𝑐
+ 3 = 8
− 3
− 3 = 4𝑐 5 4 4

9. Check!
3 𝑐+1 =8−𝑐
5 4 𝑐 =
=8− 5 4
− 5 4
15 4
+ 3 = 8

10. Check!
− 5 4
15 4
+ 3 = 8
15 4
32 4
− 5 4 =
27 4
27 4 =

11. Example 4
𝑛 2 +2=10− 𝑛 2
+ 𝑛 2
+ 𝑛 2
2𝑛 2
+ 2 = 10

12. Example 4
2𝑛 2
+ 2 = 10 𝑛
+ 2 = 10
− 2
− 2 𝑛 = 8

13. Check!
𝑛 2 +2=10− 𝑛 2 𝑛 = 8
8 2 +2=10− 8 2 4
+ 2 = 10
− 4 6 = 6