Let's solve each of these equations step by step. These are
linear equations with variables on both sides, so the goal is to isolate the variable $ x $ on one side.
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General Strategy:
1. Move all terms with $ x $ to one side.
2. Move constant terms to the other side.
3. Simplify and solve for $ x $.
---
(a) $ 4x + 1 = 2x + 7 $
Subtract $ 2x $ from both sides:
$$
4x - 2x + 1 = 7 \Rightarrow 2x + 1 = 7
$$
Subtract 1:
$$
2x = 6
$$
Divide by 2:
$$
x = 3
$$
✔ Answer: $ x = 3 $
---
(b) $ 5x + 4 = 3x + 16 $
Subtract $ 3x $:
$$
2x + 4 = 16
$$
Subtract 4:
$$
2x = 12
$$
Divide:
$$
x = 6
$$
✔ Answer: $ x = 6 $
---
(c) $ 2x + 8 = x + 12 $
Subtract $ x $:
$$
x + 8 = 12
$$
Subtract 8:
$$
x = 4
$$
✔ Answer: $ x = 4 $
---
(d) $ 7x + 1 = 2x + 46 $
Subtract $ 2x $:
$$
5x + 1 = 46
$$
Subtract 1:
$$
5x = 45
$$
Divide:
$$
x = 9
$$
✔ Answer: $ x = 9 $
---
(e) $ 6x - 3 = 2x + 13 $
Subtract $ 2x $:
$$
4x - 3 = 13
$$
Add 3:
$$
4x = 16
$$
Divide:
$$
x = 4
$$
✔ Answer: $ x = 4 $
---
(f) $ 9x - 10 = 7x + 24 $
Subtract $ 7x $:
$$
2x - 10 = 24
$$
Add 10:
$$
2x = 34
$$
Divide:
$$
x = 17
$$
✔ Answer: $ x = 17 $
---
(g) $ 2x + 21 = 4x + 5 $
Subtract $ 2x $:
$$
21 = 2x + 5
$$
Subtract 5:
$$
16 = 2x
$$
Divide:
$$
x = 8
$$
✔ Answer: $ x = 8 $
---
(h) $ x + 2 = 5x - 2 $
Subtract $ x $:
$$
2 = 4x - 2
$$
Add 2:
$$
4 = 4x
$$
Divide:
$$
x = 1
$$
✔ Answer: $ x = 1 $
---
(i) $ 6x - 9 = 4x - 1 $
Subtract $ 4x $:
$$
2x - 9 = -1
$$
Add 9:
$$
2x = 8
$$
Divide:
$$
x = 4
$$
✔ Answer: $ x = 4 $
---
(j) $ 5x + 2 = 16 - 2x $
Add $ 2x $ to both sides:
$$
7x + 2 = 16
$$
Subtract 2:
$$
7x = 14
$$
Divide:
$$
x = 2
$$
✔ Answer: $ x = 2 $
---
(k) $ 3x - 1 = 23 - x $
Add $ x $ to both sides:
$$
4x - 1 = 23
$$
Add 1:
$$
4x = 24
$$
Divide:
$$
x = 6
$$
✔ Answer: $ x = 6 $
---
(l) $ 6x + 8 = 38 - 4x $
Add $ 4x $:
$$
10x + 8 = 38
$$
Subtract 8:
$$
10x = 30
$$
Divide:
$$
x = 3
$$
✔ Answer: $ x = 3 $
---
(m) $ 80 - x = 8x - 1 $
Add $ x $ to both sides:
$$
80 = 9x - 1
$$
Add 1:
$$
81 = 9x
$$
Divide:
$$
x = 9
$$
✔ Answer: $ x = 9 $
---
(n) $ 2x + 7 = 17 - 8x $
Add $ 8x $:
$$
10x + 7 = 17
$$
Subtract 7:
$$
10x = 10
$$
Divide:
$$
x = 1
$$
✔ Answer: $ x = 1 $
---
(o) $ 15 - x = 27 - 3x $
Add $ 3x $:
$$
15 + 2x = 27
$$
Subtract 15:
$$
2x = 12
$$
Divide:
$$
x = 6
$$
✔ Answer: $ x = 6 $
---
(p) $ 12x - 20 = 15x - 38 $
Subtract $ 12x $:
$$
-20 = 3x - 38
$$
Add 38:
$$
18 = 3x
$$
Divide:
$$
x = 6
$$
✔ Answer: $ x = 6 $
---
(q) $ 35x + 10 = 20x + 175 $
Subtract $ 20x $:
$$
15x + 10 = 175
$$
Subtract 10:
$$
15x = 165
$$
Divide:
$$
x = 11
$$
✔ Answer: $ x = 11 $
---
(r) $ 14x = 2x + 60 $
Subtract $ 2x $:
$$
12x = 60
$$
Divide:
$$
x = 5
$$
✔ Answer: $ x = 5 $
---
##
✔ Final Answers:
| Question | Answer |
|--------|--------|
| (a) | $ x = 3 $ |
| (b) | $ x = 6 $ |
| (c) | $ x = 4 $ |
| (d) | $ x = 9 $ |
| (e) | $ x = 4 $ |
| (f) | $ x = 17 $ |
| (g) | $ x = 8 $ |
| (h) | $ x = 1 $ |
| (i) | $ x = 4 $ |
| (j) | $ x = 2 $ |
| (k) | $ x = 6 $ |
| (l) | $ x = 3 $ |
| (m) | $ x = 9 $ |
| (n) | $ x = 1 $ |
| (o) | $ x = 6 $ |
| (p) | $ x = 6 $ |
| (q) | $ x = 11 $ |
| (r) | $ x = 5 $ |
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Let me know if you'd like a video explanation or further practice!
Parent Tip: Review the logic above to help your child master the concept of two step equations with variables on both sides worksheet.
