1. Ch. 2 Vocabulary ( continued)
8.) identity
9.) literal equation
10.) formula

2. 2-4 Solving Equations with Variables on Both Sides
Algebra 1

3. Add an extra Step to Solving Eq.’s
After you SIMPLIFY, then you should ADD THE OPPOSITE of either variable to both sides.
Then you can ADD THE OPPOSITE of the constants or numbers without variables, etc…

4. Example 1
Solve: 5x – 6 = 3x + 9

5. Example 1 (Cont’d)
Solve: 5x – 6 = 3x + 9
-3x x Add the Opp. Of Var.

6. Example 1 (Cont’d) Solve: 5x – 6 = 3x + 9 -3x -3x Add the Opp. Of Var.

7. Example 1 (Cont’d) Solve: 5x – 6 = 3x + 9 -3x -3x Add the Opp. Of Var.
Add the Opp. Of No.’s

8. Example 1 (Cont’d) Solve: 5x – 6 = 3x + 9 -3x -3x Add the Opp. Of Var.
Add the Opp. Of No.’s
2x =

9. Example 1 (Cont’d) Solve: 5x – 6 = 3x + 9 -3x -3x Add the Opp. Of Var.
Add the Opp. Of No.’s
2x =
Divide by the coeff.

10. Example 1 (Cont’d) 5x – 6 = 3x + 9 -3x -3x Add the Opp. Of Var.
Add the Opp. Of No.’s
2x =
Divide by the coeff.
x = 7 ½ Solution

11. Example 2
Solve: 5m + 4 = 7(m + 1) – 2m

12. Example 2(Cont’d) Solve: 5m + 4 = 7(m + 1) – 2m
5m + 4 = 7m + 7 – 2m Simplify-Dist.Prop.

13. Example 2 (Cont’d) Solve: 5m + 4 = 7(m + 1) – 2m
5m + 4 = 7m + 7 – 2m Simplify-Dist.Prop.
5m + 4 = 5m Simplify-Add Like Terms

14. Example 2 (Cont’d) Solve: 5m + 4 = 7(m + 1) – 2m
5m + 4 = 7m + 7 – 2m Simplify-Dist.Prop.
5m + 4 = 5m Simplify-Add Like m m (Add the Opp.) Terms

15. Example 2 ( Cont’d) Solve: 5m + 4 = 7(m + 1) – 2m
5m + 4 = 7m + 7 – 2m Simplify-Dist.Prop.
5m + 4 = 5m Simplify-Add Like m m (Add the Opp.) Terms
does not equal 7, so there is NO Solution

16. Example 2 ( Cont’d)
No Solution can be written as a symbol, an O with a slash through it, .

17. Ex. 3)
7(4 - y) = 3(y - 4)

18. Ex. 4
2y + 4 = 2(y + 2)

19. All Real Numbers as a Solution
If you have an answer where the left side does equal the right side (4=4), then the solution involves all Real Numbers.
Usually, we represent Real Numbers as a capitalized cursive R, like .

20. Three Possible Solutions
Let’s review the three possible solutions!
x = ?
No Solution or when a number does not equal another number ( ).
All Real Numbers or when a number equals itself ( 4 = 4).