Single Variable Equation Worksheet 11 Worksheets - Free Printable

You’ve uploaded a worksheet titled “Solve the Single Variable Equations” from an Algebra section. The goal is to solve each of the 10 equations for the variable (either `x` or `y`). I’ll solve each one step-by-step and explain the reasoning.

---

Equation 1: `1 - (x + 7) = 0`

Step 1: Distribute the negative sign:
> `1 - x - 7 = 0`

Step 2: Combine like terms:
> `-x - 6 = 0`

Step 3: Add 6 to both sides:
> `-x = 6`

Step 4: Multiply both sides by -1:
> `x = -6`

✔ Answer: `x = -6`

---

Equation 2: `2 + x/12 = 2`

Step 1: Subtract 2 from both sides:
> `x/12 = 0`

Step 2: Multiply both sides by 12:
> `x = 0`

✔ Answer: `x = 0`

---

Equation 3: `8 - x = 7`

Step 1: Subtract 8 from both sides:
> `-x = -1`

Step 2: Multiply both sides by -1:
> `x = 1`

✔ Answer: `x = 1`

---

Equation 4: `7 + 1 · y = 12`

Note: `1 · y` is just `y`.

Step 1: Simplify:
> `7 + y = 12`

Step 2: Subtract 7 from both sides:
> `y = 5`

✔ Answer: `y = 5`

---

Equation 5: `9 + y + 8 = 98`

Step 1: Combine constants:
> `17 + y = 98`

Step 2: Subtract 17 from both sides:
> `y = 81`

✔ Answer: `y = 81`

---

Equation 6: `11 + y/10 = 12`

Step 1: Subtract 11 from both sides:
> `y/10 = 1`

Step 2: Multiply both sides by 10:
> `y = 10`

✔ Answer: `y = 10`

---

Equation 7: `4 + x + 4 = 20`

Step 1: Combine constants:
> `8 + x = 20`

Step 2: Subtract 8 from both sides:
> `x = 12`

✔ Answer: `x = 12`

---

Equation 8: `2 + 8 · x = 66`

Step 1: Subtract 2 from both sides:
> `8x = 64`

Step 2: Divide both sides by 8:
> `x = 8`

✔ Answer: `x = 8`

---

Equation 9: `11 + 1 + x = 23`

Step 1: Combine constants:
> `12 + x = 23`

Step 2: Subtract 12 from both sides:
> `x = 11`

✔ Answer: `x = 11`

---

Equation 10: `3 - y = 0`

Step 1: Subtract 3 from both sides:
> `-y = -3`

Step 2: Multiply both sides by -1:
> `y = 3`

✔ Answer: `y = 3`

---

## ✔ Final Answers:

1. x = -6
2. x = 0
3. x = 1
4. y = 5
5. y = 81
6. y = 10
7. x = 12
8. x = 8
9. x = 11
10. y = 3

---

Let me know if you’d like these formatted as a completed worksheet or need help with graphing, checking your work, or understanding any step!