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Solving and Graphing Inequalities

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Solving and Graphing Inequalities Assessment

Mathematical inequality symbols and number line

📚 Part 1: Multiple Choice

Instructions: Choose the best answer for each question. Fill in the circle completely.

1. Which inequality symbol means "greater than or equal to"?

A) >

B) <

C) ≥

D) ≤

2. Solve: x + 5 > 12

A) x > 7

B) x > 17

C) x < 7

D) x < 17

3. When graphing x ≤ -3 on a number line, what type of circle should be drawn at -3?

A) Open circle

B) Closed circle

C) No circle

D) Square

4. Solve: 3x < 15

A) x < 5

B) x > 5

C) x < 45

D) x > 45

5. Which value is NOT a solution to x ≥ 4?

A) 4

B) 5

C) 3

D) 10

✏️ Part 2: Problem Solving

Instructions: Show your work and write your final answer clearly.

6. Solve the inequality: 2x - 7 ≤ 9

Show your work:

Final Answer: x _____________

7. Graph the solution to x > -2 on the number line below. Draw and label your number line.
8. Maria has $25 to spend on books. Each book costs $4. Write and solve an inequality to find the maximum number of books she can buy. Explain your answer in complete sentences.

Inequality: _____________________

Answer and Explanation:

📋 Answer Key

Part 1 - Multiple Choice:

1. C) ≥

2. A) x > 7

3. B) Closed circle

4. A) x < 5

5. C) 3

Part 2 - Problem Solving:

6. x ≤ 8 (Work: Add 7 to both sides: 2x ≤ 16, then divide by 2: x ≤ 8)

7. Number line with open circle at -2, arrow pointing right

8. Inequality: 4b ≤ 25; Solution: b ≤ 6.25, so Maria can buy at most 6 books

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