Worksheet for solving one-step equations and inequalities.

It looks like you've uploaded a worksheet titled "Equations WS1" that contains 18 algebraic equations to solve for the variable. Since I can't view images directly, I'll help you solve each equation step by step based on the text you provided.

Let me go through each problem and solve it with clear explanations:

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1. $ \frac{x}{8} = 10 $

To solve for $ x $, multiply both sides by 8:
$$
x = 10 \times 8 = 80
$$
✔ Answer: $ x = 80 $

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2. $ x - 12 = -12 $

Add 12 to both sides:
$$
x = -12 + 12 = 0
$$
✔ Answer: $ x = 0 $

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3. $ x + 50 = 62 $

Subtract 50 from both sides:
$$
x = 62 - 50 = 12
$$
✔ Answer: $ x = 12 $

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4. $ 43 = x - 23 $

Add 23 to both sides:
$$
x = 43 + 23 = 66
$$
✔ Answer: $ x = 66 $

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5. $ 307 = x + 318 $

Subtract 318 from both sides:
$$
x = 307 - 318 = -11
$$
✔ Answer: $ x = -11 $

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6. $ y - (-10) = 49 $

Simplify: subtracting a negative is adding:
$$
y + 10 = 49
$$
Subtract 10:
$$
y = 49 - 10 = 39
$$
✔ Answer: $ y = 39 $

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7. $ 2x = 16 $

Divide both sides by 2:
$$
x = \frac{16}{2} = 8
$$
✔ Answer: $ x = 8 $

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8. $ 4p = 88 $

Divide both sides by 4:
$$
p = \frac{88}{4} = 22
$$
✔ Answer: $ p = 22 $

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9. $ \frac{m}{12} = 7 $

Multiply both sides by 12:
$$
m = 7 \times 12 = 84
$$
✔ Answer: $ m = 84 $

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10. $ -6x + 72 = -30 $

Subtract 72 from both sides:
$$
-6x = -30 - 72 = -102
$$
Divide by -6:
$$
x = \frac{-102}{-6} = 17
$$
✔ Answer: $ x = 17 $

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11. $ 7x - 3 = -9 $

Add 3 to both sides:
$$
7x = -9 + 3 = -6
$$
Divide by 7:
$$
x = \frac{-6}{7}
$$
✔ Answer: $ x = -\frac{6}{7} $

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12. $ 8x + 2x = 15 $

Combine like terms:
$$
10x = 15
$$
Divide by 10:
$$
x = \frac{15}{10} = \frac{3}{2} = 1.5
$$
✔ Answer: $ x = \frac{3}{2} $ or $ 1.5 $

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13. $ 7.3x = 19.01 $

Divide both sides by 7.3:
$$
x = \frac{19.01}{7.3} \approx 2.6
$$

Let’s check: $ 7.3 \times 2.6 = 18.98 $ → close, but let's do exact:

$$
x = \frac{19.01}{7.3} = 2.6041...
$$

But likely intended as:
$$
x = \frac{19.01}{7.3} = 2.6 \quad \text{(rounded)}
$$

But better to keep exact:
$$
x = \frac{1901}{730} \quad \text{(multiply numerator and denominator by 100)}
$$

But unless specified, we can write:
✔ Answer: $ x \approx 2.6 $ (or $ x = 2.604 $ if more precision)

Wait — let's check:
$ 7.3 \times 2.6 = 18.98 $, so difference of 0.03 → maybe typo?

Alternatively, perhaps it's meant to be exact. Let's assume:
$$
x = \frac{19.01}{7.3} = \frac{1901}{730} \approx 2.604
$$

But since it's likely a decimal problem, accept:
✔ Answer: $ x \approx 2.6 $ (but ideally use calculator for exact value)

Actually, let's compute:
$$
19.01 ÷ 7.3 = ?
$$
Multiply numerator and denominator by 10:
$$
190.1 ÷ 73 ≈ 2.6041...
$$

So:
✔ Answer: $ x \approx 2.60 $ (to two decimals)

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14. $ 3a + 18 = -99 $

Subtract 18:
$$
3a = -99 - 18 = -117
$$
Divide by 3:
$$
a = \frac{-117}{3} = -39
$$
✔ Answer: $ a = -39 $

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15. $ 10n - 60 = 31 $

Add 60:
$$
10n = 31 + 60 = 91
$$
Divide by 10:
$$
n = \frac{91}{10} = 9.1
$$
✔ Answer: $ n = 9.1 $

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16. $ -4x + 8 = 40 $

Subtract 8:
$$
-4x = 40 - 8 = 32
$$
Divide by -4:
$$
x = \frac{32}{-4} = -8
$$
✔ Answer: $ x = -8 $

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17. $ \frac{b}{3} - 5 = 6 $

Add 5:
$$
\frac{b}{3} = 11
$$
Multiply by 3:
$$
b = 11 \times 3 = 33
$$
✔ Answer: $ b = 33 $

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18. $ \frac{5}{6} + x = 12 $

Subtract $ \frac{5}{6} $:
$$
x = 12 - \frac{5}{6} = \frac{72}{6} - \frac{5}{6} = \frac{67}{6}
$$
✔ Answer: $ x = \frac{67}{6} $ or $ 11\frac{1}{6} $

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## ✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $ x = 80 $ |
| 2 | $ x = 0 $ |
| 3 | $ x = 12 $ |
| 4 | $ x = 66 $ |
| 5 | $ x = -11 $ |
| 6 | $ y = 39 $ |
| 7 | $ x = 8 $ |
| 8 | $ p = 22 $ |
| 9 | $ m = 84 $ |
|10 | $ x = 17 $ |
|11 | $ x = -\frac{6}{7} $ |
|12 | $ x = \frac{3}{2} $ or $ 1.5 $ |
|13 | $ x \approx 2.60 $ |
|14 | $ a = -39 $ |
|15 | $ n = 9.1 $ |
|16 | $ x = -8 $ |
|17 | $ b = 33 $ |
|18 | $ x = \frac{67}{6} $ or $ 11\frac{1}{6} $ |

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