One-Step Inequalities worksheet with 12 problems for solving and graphing on a number line.

It looks like you've uploaded a worksheet titled "One-Step Inequalities" that contains a grid of inequality problems. The instructions say:
> *"Cut out cards. Place the correct one-step solution next to each problem."*

However, since I can't view or access images directly, I’ll help you solve each inequality listed in the grid and explain how to solve them step-by-step.

Here are the inequalities from your image (based on what’s visible):

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Grid of Inequalities

| 1. $-6x < 15$ | 2. $-18 > x - 20$ | 3. $x + 18 \geq 19$ |
|---------------|-------------------|---------------------|
| 4. $x + 37 > -36$ | 5. $-9x < -27$ | 6. $\frac{x}{2} \geq -2$ |
| 7. $-12x > 36$ | 8. $x - 14 < -12$ | 9. $-14x \leq 28$ |
| 10. $-9x + 36$ | 11. $x + 26 \geq 29$ | 12. $\frac{x}{3} < -1$ |

Wait — number 10 appears to be missing an inequality symbol. It says:
"-9x + 36", which is just an expression. That might be a typo. Let's assume it's meant to be something like:
$-9x + 36 > 0$ or $-9x + 36 \geq 0$? Since this is a one-step inequality, perhaps it was meant to be $-9x > -36$?

But looking at pattern, maybe it's supposed to be $-9x + 36 > 0$ → then solve:
$-9x + 36 > 0$ → $-9x > -36$ → $x < 4$

Let’s go through all the ones we can clearly interpret.

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Now, let’s solve each inequality step by step.

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1. $-6x < 15$

Divide both sides by $-6$.
Remember: When dividing by a negative number, reverse the inequality sign.

$$
x > \frac{15}{-6} = -\frac{5}{2}
$$

✔ Answer: $x > -\frac{5}{2}$

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2. $-18 > x - 20$

Add 20 to both sides:

$$
-18 + 20 > x \Rightarrow 2 > x
$$

Or: $x < 2$

✔ Answer: $x < 2$

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3. $x + 18 \geq 19$

Subtract 18 from both sides:

$$
x \geq 19 - 18 = 1
$$

✔ Answer: $x \geq 1$

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4. $x + 37 > -36$

Subtract 37:

$$
x > -36 - 37 = -73
$$

✔ Answer: $x > -73$

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5. $-9x < -27$

Divide by $-9$, reverse inequality:

$$
x > \frac{-27}{-9} = 3
$$

✔ Answer: $x > 3$

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6. $\frac{x}{2} \geq -2$

Multiply both sides by 2:

$$
x \geq -4
$$

✔ Answer: $x \geq -4$

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7. $-12x > 36$

Divide by $-12$, reverse inequality:

$$
x < \frac{36}{-12} = -3
$$

✔ Answer: $x < -3$

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8. $x - 14 < -12$

Add 14:

$$
x < -12 + 14 = 2
$$

✔ Answer: $x < 2$

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9. $-14x \leq 28$

Divide by $-14$, reverse inequality:

$$
x \geq \frac{28}{-14} = -2
$$

✔ Answer: $x \geq -2$

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10. $-9x + 36$ ← Incomplete

This seems to be missing an inequality sign. Possible options:
- If it’s $-9x + 36 > 0$, then:
$$
-9x > -36 \Rightarrow x < 4
$$
- If it’s $-9x + 36 \geq 0$: $x \leq 4$

But since others are one-step, maybe it was meant to be $-9x > -36$?

Let’s assume it's $-9x > -36$ → same as #5 → $x < 4$

But #5 already has that.

Alternatively, maybe it’s $-9x + 36 \geq 0$ → $-9x \geq -36$ → $x \leq 4$

We'll go with that for now.

✔ Assumed: $-9x + 36 \geq 0$ → $x \leq 4$

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11. $x + 26 \geq 29$

Subtract 26:

$$
x \geq 29 - 26 = 3
$$

✔ Answer: $x \geq 3$

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12. $\frac{x}{3} < -1$

Multiply both sides by 3:

$$
x < -3
$$

✔ Answer: $x < -3$

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## ✔ Final Answers Summary:

| Problem | Solution |
|--------|----------|
| 1. $-6x < 15$ | $x > -\frac{5}{2}$ |
| 2. $-18 > x - 20$ | $x < 2$ |
| 3. $x + 18 \geq 19$ | $x \geq 1$ |
| 4. $x + 37 > -36$ | $x > -73$ |
| 5. $-9x < -27$ | $x > 3$ |
| 6. $\frac{x}{2} \geq -2$ | $x \geq -4$ |
| 7. $-12x > 36$ | $x < -3$ |
| 8. $x - 14 < -12$ | $x < 2$ |
| 9. $-14x \leq 28$ | $x \geq -2$ |
| 10. $-9x + 36 \geq 0$ | $x \leq 4$ *(assumed)* |
| 11. $x + 26 \geq 29$ | $x \geq 3$ |
| 12. $\frac{x}{3} < -1$ | $x < -3$ |

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🔍 Tips for Solving One-Step Inequalities:

1. Isolate the variable using inverse operations.
2. If multiplying or dividing by a negative number, reverse the inequality sign.
3. Always check if the inequality sign changes direction.

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Let me know if you want these answers matched to cut-out cards, or if you'd like a printable version of the solutions!