Multi-Step Inequalities Quiz

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Date:

📚 Part 1: Multiple Choice & Learning Targets

I can... solve multi-step inequalities, including those with distribution and variables on both sides, and graph solutions on a number line.

Success criteria: Show algebraic steps, reverse the inequality when multiplying/dividing by a negative, and draw the correct inequality on a number line.

Differentiation strategies: Provide step templates for students who need structure; offer guided pairs for practice; allow calculators for arithmetic if needed.

1. Solve: 3(x - 2) > 9. Which is the correct solution?

x > 3

x > 5

x < 5

x ≥ 5

2. Solve: -2x + 7 ≤ 15. Which is the correct solution?

x ≤ -4

x ≥ -4

x < 4

x > -4

3. Jason has $20 for a taxi. The fare is $2.50 plus $1.20 per mile. Let m be miles. For how many miles can he ride so cost ≤ $20?

m ≤ 14.58

m ≥ 14.58

m < 14

m > 14

4. Solve the compound inequality: 1 ≤ 2x + 3 < 9. Which represents the solution?

-1 < x ≤ 3

-1 ≤ x < 3

-1 ≤ x ≤ 3

x > -1

✏️ Part 2: Short Answer (Solve, Show Work, Graph)

5. Solve and show steps: 4 - 3x ≥ 10. Then graph the solution on the number line.

6. Solve and show steps: -0.5(2x - 8) < 3. Write the final inequality.

7. Solve and show steps: 5x + 4 ≤ 2x + 16. State the solution set.

8. A storage unit allows at most 1,500 pounds. Each box weighs 28 lb. You already have 32 boxes. Let b be how many more boxes you can add. Write and solve an inequality for b. How many whole boxes can you add?

Extension (for advanced learners): Create a real-world inequality involving temperature (°F) or distance (miles) that requires distributing, combining like terms, and solving a compound inequality. Provide the context and solution.

Dyslexia-friendly reading options: Allow students the choice of a colored overlay, provide questions in larger font, read questions aloud, or give extra time. Provide one worked example using step labels (Step 1, Step 2, Step 3).