Equations Worksheet 1 featuring six algebraic equations for solving, with an answer key section.

I'll solve each equation step by step, working through them carefully.

1a. 3 + x = 6
- Subtract 3 from both sides: x = 6 - 3
- x = 3

1b. z + 10 = 5
- Subtract 10 from both sides: z = 5 - 10
- z = -5

2a. 11 = 2 + n
- Subtract 2 from both sides: 11 - 2 = n
- 9 = n (or n = 9)

2b. 4 = r - 1
- Add 1 to both sides: 4 + 1 = r
- 5 = r (or r = 5)

3a. 9 = 10y - 7y
- Combine like terms on the right: 9 = 3y
- Divide both sides by 3: y = 9 3
- y = 3

3b. t/9 = 1 - 12
- Simplify the right side: t/9 = -11
- Multiply both sides by 9: t = -11 × 9
- t = -99

4a. 7 = y/10
- Multiply both sides by 10: 7 × 10 = y
- 70 = y (or y = 70)

4b. b - 5 = 7 · 4
- First calculate 7 · 4 = 28
- So: b - 5 = 28
- Add 5 to both sides: b = 28 + 5
- b = 33

5a. 5 = x/9
- Multiply both sides by 9: 5 × 9 = x
- 45 = x (or x = 45)

5b. z + 7 = 6
- Subtract 7 from both sides: z = 6 - 7
- z = -1

6a. 12u - 8u = 12
- Combine like terms: 4u = 12
- Divide both sides by 4: u = 12 ÷ 4
- u = 3

6b. r + 10 = 9
- Subtract 10 from both sides: r = 9 - 10
- r = -1

Final Answer:
1a. x = 3
1b. z = -5
2a. n = 9
2b. r = 5
3a. y = 3
3b. t = -99
4a. y = 70
4b. b = 33
5a. x = 45
5b. z = -1
6a. u = 3
6b. r = -1