This worksheet provides twelve practice problems for students to solve single-step algebraic equations for the variable x.

It looks like you've uploaded a worksheet titled "Solving Equations (single step equations) Worksheet 1", which contains a series of simple algebraic equations that need to be solved for the variable $ x $. I'll solve each equation step-by-step and explain the process.

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🔷 Instructions:

Solve each equation for $ x $. Show your work.

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Let's go through each problem:

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1.) $ x + 9 = 16 $

To solve for $ x $, subtract 9 from both sides:
$$
x + 9 - 9 = 16 - 9 \\
x = 7
$$

✔ Answer: $ x = 7 $

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2.) $ x - 7 = 1 $

Add 7 to both sides:
$$
x - 7 + 7 = 1 + 7 \\
x = 8
$$

✔ Answer: $ x = 8 $

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3.) $ x + 4 = 10 $

Subtract 4 from both sides:
$$
x + 4 - 4 = 10 - 4 \\
x = 6
$$

✔ Answer: $ x = 6 $

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4.) $ x - 8 = 6 $

Add 8 to both sides:
$$
x - 8 + 8 = 6 + 8 \\
x = 14
$$

✔ Answer: $ x = 14 $

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5.) $ x - 18 = 20 $

Add 18 to both sides:
$$
x - 18 + 18 = 20 + 18 \\
x = 38
$$

✔ Answer: $ x = 38 $

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6.) $ x \div 2 = 1 $

Multiply both sides by 2:
$$
2 \cdot (x \div 2) = 1 \cdot 2 \\
x = 2
$$

✔ Answer: $ x = 2 $

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7.) $ x \div 7 = 1 $

Multiply both sides by 7:
$$
7 \cdot (x \div 7) = 1 \cdot 7 \\
x = 7
$$

✔ Answer: $ x = 7 $

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8.) $ x \div 7 = 9 $

Multiply both sides by 7:
$$
7 \cdot (x \div 7) = 9 \cdot 7 \\
x = 63
$$

✔ Answer: $ x = 63 $

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9.) $ x \div 2 = 7 $

Multiply both sides by 2:
$$
2 \cdot (x \div 2) = 7 \cdot 2 \\
x = 14
$$

✔ Answer: $ x = 14 $

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10.) $ 3x = 12 $

Divide both sides by 3:
$$
\frac{3x}{3} = \frac{12}{3} \\
x = 4
$$

✔ Answer: $ x = 4 $

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11.) $ 4x + 1 = 18 $

First, subtract 1 from both sides:
$$
4x + 1 - 1 = 18 - 1 \\
4x = 17
$$

Now divide both sides by 4:
$$
x = \frac{17}{4} = 4.25
$$

✔ Answer: $ x = \frac{17}{4} $ or $ 4.25 $

> Note: This is still a single-step equation if we consider "undoing" addition first, then division — but technically it's two steps. However, since the worksheet says "single step", this might be an error in labeling. But let’s assume it's allowed.

Alternatively, if only one operation is involved (like just multiplication/division or addition/subtraction), then these are single-step. So perhaps #11 is not truly single-step.

But let's continue.

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12.) $ 4x = 8 $

Divide both sides by 4:
$$
\frac{4x}{4} = \frac{8}{4} \\
x = 2
$$

✔ Answer: $ x = 2 $

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1.) | $ x = 7 $ |
| 2.) | $ x = 8 $ |
| 3.) | $ x = 6 $ |
| 4.) | $ x = 14 $ |
| 5.) | $ x = 38 $ |
| 6.) | $ x = 2 $ |
| 7.) | $ x = 7 $ |
| 8.) | $ x = 63 $ |
| 9.) | $ x = 14 $ |
| 10.) | $ x = 4 $ |
| 11.) | $ x = \frac{17}{4} $ or $ 4.25 $ |
| 12.) | $ x = 2 $ |

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📝 Explanation of Method:

- For addition/subtraction equations (e.g., $ x + a = b $), isolate $ x $ by doing the inverse operation (subtract $ a $).
- For multiplication/division equations (e.g., $ ax = b $), isolate $ x $ by dividing both sides by $ a $.
- Always perform the same operation on both sides to keep the equation balanced.

Let me know if you'd like this formatted as a printable answer sheet!