1. Bell Ringer

2. Equations with Variables on Both Sides
Mr. Haupt
CC A.2; CC A.3

3. Combine Like Terms ONLY
There is no real difference in how we solve equations with variables on both sides.
You just have to make sure when you move the variable and its coefficient you only add or subtract it from another variable. For example, you cannot add 5x to 7. you can only add 5x to 7x.
Two special cases when we solve equations with variables on both sides.
Identity
No Solution

4. Identity
An Identity solution is when the equation will work for any possible number.
You will know these when you see them because when you solve them you will end up with the same thing on both sides of the equal sign.
For example: 2x = 2x
Any number you plug into x will work.

5. No Solution No Solution is the opposite of Identity.
When there is no solution, it means that no matter what value you plug in for the variable, you cannot solve the equation.
For example: 6x +1 = 6x – 8

6. Example 1

7. Example 2

8. Example 3

9. Proportions

10. Proportions Proportions are simply comparing fractions.
We use these a lot in life and when we do unit rates.
For example, if you want to buy sliced cheese at the deli, and it is 8 dollars a pound and you want 3 pounds, how would you figure that out?

11. Solving Proportions Solving them is easy.
Cross multiply and then divide.