Lesson 12: more on Equations

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!

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

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

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

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

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

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

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

Check! − 5 4 15 4 + 3 = 8 15 4 + 12 4 32 4 − 5 4 = 27 4 27 4 =

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

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

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