1. Solving Equations with Variables on Both Sides

2. Example Solve. Check. 10a 10a = 7a + 21 10a = 7a+ 21 7a – 7a – 7a
10(7) = 7(7)+ 21 3 3a = 21
70 = 3 3
70 = 70  7 a =

3. Example Solve. Check. 5x 5x = 9x 9x + 32 5x = 9x + 32 – 9x – 9x
5(-8) = 9(-8)+ 32
-4x -4 = 32
-40 = -4 -4
-40 =- 40  x = -8

4. Example (Same problem)
Solve.
Check. 5x 5x = 9x 9x
+ 32
5x = 9x + 32
– 5x
– 5x
5(-8) = 9(-8)+ 32 = 4x
+ 32
- 32
- 32
-40 = = 4x
- 32
-40 = -40  4 4 -8 = x

5. Example Solve. Check. 12x 12x = 7x 7x + 45 12x = 7x + 45 – 7x - 7x
12(9) = 7(9)+ 45 5x 5 = 45
108 = 5 5
108 = 108  x = 9

6. Example Solve. Check. 5x 3x - 1 5x + 1 = 3x - 1 5x + 1 = 3x -3x -3x
4(-1)+1 = 3(-1)- 1 2x
+ 1
+ 1 = -1 -1 =
- 1 -1 2x = -2
-4 = -4  2 2
x = -1

7. Example Solve. Check. -x -x + 3 -3x + 9 -x + 3 = -3x + 9 = -3x +3x +3x
-(3)+3 = -3(3) + 9 2x
+ 3
+ 3 = +9 +9
0 =
- 3
- 3 2x = 6
0 = 0  2 2
x = 3

8. Example 8x + 2 (3x + 5) = 7x + 10 8x + 8x 6x 6x + 10 = 7x + 10 7x 7x
- 10
- 10 7x = 7 7
x = 0

9. Check 8x + 2 (3x + 5) = 7x + 10 8(0) + 2[3(0) + 5] = 7(0) + 10
[ ] =
[ 5] = 10
= 10
10 = 10 