1. Equations with variables on both sides Whiteboard practice

2. 9b – 6 = 5b + 18
b = 6
9b – 6 = 5b + 18
– 5b – 5b
Subtract 5b from both sides.
4b – 6 = 18
Add 6 to both sides.
4b = 24 4b 4 24 =
Divide both sides by 4.
b = 6

3. a + 5 = -5a + 5 a = 0 a + 5 = -5a + 5 +5a + 5a Add 5a to both sides.
Subtract 5 from both sides.
6a = 0 6a 6 =
Divide both sides by 4.
a = 0

4. 3b – 2 = 2b + 12
b = 14
3b – 2 = 2b + 12
– 2b – 2b
Subtract 2b from both sides.
b – 2 =
Add 2 to both sides.
b = 14

5. 2x + 1 = x - 7
x = -8
2x + 1 = x - 7
– 1x – 1x
Subtract 1x from both sides.
1x + 1 = -7
Subtract 1 from both sides.
x = -8

6. 5p – 14 = 8p + 4
p = -6
5p – 14 = 8p + 4
– 8p – 8p
Subtract 8p from both sides.
-3p =
Add 14 to both sides.
-3p = 18
Divide both sides by -3.
p = -6

7. x = 2 3x+ 6 = 6x 3x + 6 = 6x – 6x = –6x Subtract 6x from both sides.
- 6 = -6
Subtract 6 from both sides.
-3x = -6
-3 = -3
Divide both sides by -3
x = 2

8. 9w + 3 = 9w + 7
3 ≠ 7 (no solution)
9w + 3 = 9w + 7
– 9w – 9w
Subtract 9w from both sides.
3 ≠ 7
No solution. There is no number that can be substituted for the variable w to make the equation true.

9. 8x– 2 = -9 + 7x x = -7 8x – 2 = -9 + 7x Subtract 7x from both sides.
Add 2 to both sides.
x = -7

10. x = 4 8 + x = 3x 8 + x = 3x – 3x = – 3x Subtract 3x from both sides.
= -8
Subtract 8 from both sides.
-2x = -8
-2 = -2
Divide both sides by -2.
x = 4

11. 2b + 5 = 4b - 1
b = 3
2b + 5 = 4b - 1
– 4b – 4b
Subtract 4b from both sides.
-2b + 5 =
Subtract 5 from both sides.
-2b =
-2b = -6
Divide both sides by -2.
-2 = -2
b = 3

12. x + 2 = 2x - 3
x = 5
x + 2 = 2x - 3
– 2x – 2x
Subtract 2x from both sides.
-1x + 2 = -3
Subtract 2 from both sides.
-1x =
-1x = -5
Divide both sides by -1.
-1 = -1
x = 5

13. n = -3 5n + 9 = 2n 5n + 9 = 2n – 2n = –2n Subtract 2n from both sides.
- 9 = -9
Subtract 9 from both sides.
3n = -9
3 = 3
Divide both sides by 3.
n = -3

14. 1 ≠ 8 (no solution) 3w + 1 = 3w + 8 3w + 1 = 3w + 8 – 3w – 3w
1 ≠ 8
(no solution)
3w + 1 = 3w + 8
– 3w – 3w
Subtract 3w from both sides.
1 ≠ 8
No solution. There is no number that can be substituted for the variable w to make the equation true.

15. 8y - 3 = 6y + 17
y = 10
8y - 3 = 6y + 17
– 6y – 6y
Subtract 6y from both sides.
2y - 3 = 17
Add 3 to both sides.
2y =
2y = 20
Divide both sides by 2.
2 = 2
y = 10

16. 2x + 7 = 3x + 4
x = 3
2x + 7 = 3x + 4
– 3x – 3x
Subtract 3x from both sides.
-1x + 7 = 4
Subtract 7 from both sides.
-1x = -3
-1x = -3
Divide both sides by -1.
-1 = -1
x = 3

17. -4(-6x – 3) =12
x = 0

18. 5n + 34 =-2(1-7n)
n = 4

19. 12 = -4(-6x – 3)
x = 0

20. -(-4x+7)= 9
x = 4

21. 6(1+3k)=-18-6k
k = -1

22. 3a – 5 = -8(6 +5a)
a = -1

23. 14 = -(p – 8)
p = -6

24. 2(4x – 3)-8 = 4 + 2x
x = 3

25. -(1 + 7x)-6(-7-x)= 36
x = 5