1. Exercise
Solve and check x – 3 = 5.
x = 8
8 – 3 = 5

2. Exercise
Solve and check 2x – 3 = 5.
x = 4
2(4) – 3 = 5

3. Exercise Solve and check 5x + 2 – 3x – 4 = – 2. x = 0
5(0) + 2 – 3(0) – 4 = – 2

4. Exercise Solve and check 12 = x + 4 – 3x. x = – 4
12 = – – 3(– 4)

5. Exercise
Solve and check (x – 2) + 18 = 12.
x = 0
3(0 – 2) + 18 = 12

6. Example 1 Solve and check 7x = 16 + 5x. 7x – 5x = 16 + 5x – 5x 2x = 16
7(8) = (8)
56 = 56

7. Example 2 Solve and check 8x + 5 = x. 8x + 5 – 8x = x – 8x 5 = – 7x
5 7
8(– ) + 5 = –
5 7
5 7
– = –

8. Example
Solve 5a = 3a – 8.
a = – 4

9. Example
Solve 2b + 12 = 3b + 8.
b = 4

10. Example
Solve 6n = 3(n + 7).
n = 7

11. Example 3 2x – 2x + 9 = 5x – 2x – 3 9 = 3x – 3 9 + 3 = 3x – 3 + 3
Solve and check 2x + 9 = 5x – 3.
2x – 2x + 9 = 5x – 2x – 3
9 = 3x – 3
9 + 3 = 3x – 3 + 3
12 = 3x 3
x = 4
2(4) + 9 = 5(4) – 3
17 = 17

12. Example 4 7x – 5 – 3x = 3x + 10 – 3x 4x – 5 = 10 4x – 5 + 5 = 10 + 5
Solve and check 7x – 5 = 3x + 10.
7x – 5 – 3x = 3x + 10 – 3x
4x – 5 = 10
4x – =
x =
15 4
4x = 15 4
7( ) – 5 = 3( ) + 10
15 4
85 4 =

13. Example 5 Solve and check 4(x – 3) = – 2(3x + 11). 4x – 12 = – 6x – 2210

14. Example 5 Solve and check 4(x – 3) = – 2(3x + 11). 10x = – 10 10 10
4(– 1 – 3) = – 2[ 3(– 1) + 11)]
– 16 = – 16

15. Steps in Solving an Equation
Eliminate parentheses by distributing.
Simplify each side by adding like terms.
Isolate the variable on one (either) side.

16. Steps in Solving an Equation
4. “Undo” additions to or subtractions from the variable term.
5. “Undo” multiplications or divisions of the variable.

17. Example 6 Solve – 3(x + 4) – 8 = 3x + 4. – 3x – 12 – 8 = 3x + 4
– 6

18. Example
Solve 2m + 17 = – (5m – 2).
m = –
15 7

19. Example
Solve 3(r + 2) = – 2(3r – 3).
r = 0

20. Example
Solve 3(x + 5) – 4 = 2(4x + 5).
x =
1 5

21. Example
Solve 3[x – 2(x + 1)] = 3x + 12.
x = – 3

22. Example
Solve 9.5(n + 2) = 4.4(1.5n + 12) – 1.9.
n = 11

23. Example
3 4
2 3
1 6
Solve (w + 2) = 4( w – ).
w =
26 23

24. Exercise
5 7
2 7
Solve k + 4 = k + 13.
k = 21

25. Exercise
7 9
2 9
Solve v – 2 = v + 8.
v = 18

26. Exercise
1 5
2 3
Solve 4( y – 1) = y + 17.
y =
315 2