Math worksheet for solving algebraic equations with variables.

Let’s solve each equation one by one. We’ll find the value of each letter (variable) that makes the equation true.

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1) a - 1 = 7
Add 1 to both sides:
a = 7 + 1 → a = 8

2) b + 2 = 12
Subtract 2 from both sides:
b = 12 - 2 → b = 10

3) 2 × c = 14
Divide both sides by 2:
c = 14 ÷ 2 → c = 7

4) d + 4 = 14
Subtract 4 from both sides:
d = 14 - 4 → d = 10

5) e - 2 = 5
Add 2 to both sides:
e = 5 + 2 → e = 7

6) f × 3 = 12
Divide both sides by 3:
f = 12 ÷ 3 → f = 4

7) g + 4 = 17
Subtract 4 from both sides:
g = 17 - 4 → g = 13

8) h - 2 = 12
Add 2 to both sides:
h = 12 + 2 → h = 14

9) 10 - i = 3
Subtract 10 from both sides? Wait — better to think:
What number subtracted from 10 gives 3?
i = 10 - 3 → i = 7

10) j - 8 = 7
Add 8 to both sides:
j = 7 + 8 → j = 15

11) 2k = 8
Divide both sides by 2:
k = 8 ÷ 2 → k = 4

12) l - 6 = 11
Add 6 to both sides:
l = 11 + 6 → l = 17

13) 12 - m = 2
What number subtracted from 12 gives 2?
m = 12 - 2 → m = 10

14) 4n = 28
Divide both sides by 4:
n = 28 ÷ 4 → n = 7

15) o ÷ 2 = 6
Multiply both sides by 2:
o = 6 × 2 → o = 12

16) p ÷ 5 = 4
Multiply both sides by 5:
p = 4 × 5 → p = 20

17) q / 4 = 6
Same as q ÷ 4 = 6 → Multiply both sides by 4:
q = 6 × 4 → q = 24

18) 5r = 30
Divide both sides by 5:
r = 30 ÷ 5 → r = 6

19) s - 12 = 7
Add 12 to both sides:
s = 7 + 12 → s = 19

20) 20 - t = 11
What number subtracted from 20 gives 11?
t = 20 - 11 → t = 9

21) 6u = 24
Divide both sides by 6:
u = 24 ÷ 6 → u = 4

22) v - 6 = 3
Add 6 to both sides:
v = 3 + 6 → v = 9

23) 20 ÷ w = 4
This means: 20 divided by what number equals 4?
w = 20 ÷ 4 → w = 5

24) 7x = 14
Divide both sides by 7:
x = 14 ÷ 7 → x = 2

25) 5 - y = -1
We need to find y so that when we subtract it from 5, we get -1.
Think: 5 minus what equals -1?
That means y must be bigger than 5.
5 - y = -1 → Add y to both sides: 5 = y - 1
Then add 1 to both sides: 6 = y → y = 6

Wait — let’s check:
5 - 6 = -1 → YES! Correct.

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Final Answer:

1) a = 8
2) b = 10
3) c = 7
4) d = 10
5) e = 7
6) f = 4
7) g = 13
8) h = 14
9) i = 7
10) j = 15
11) k = 4
12) l = 17
13) m = 10
14) n = 7
15) o = 12
16) p = 20
17) q = 24
18) r = 6
19) s = 19
20) t = 9
21) u = 4
22) v = 9
23) w = 5
24) x = 2
25) y = 6