Inequality worksheet for students to practice reading and representing inequalities on number lines.

Let's solve this step by step. The worksheet is divided into two sections:

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Section A: State the inequality represented on the number lines

We need to interpret each number line and write the correct inequality.

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1)
- Closed circle at 1, arrow going to the right.
- This means $ x \geq 1 $

✔ Answer: $ x \geq 1 $

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2)
- Open circle at 3, arrow going to the left.
- This means $ x < 3 $

✔ Answer: $ x < 3 $

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3)
- Open circle at -1, arrow going to the right.
- This means $ x > -1 $

✔ Answer: $ x > -1 $

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4)
- Closed circle at -3, arrow going to the right.
- This means $ x \geq -3 $

✔ Answer: $ x \geq -3 $

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5)
- Closed circle at -2, arrow going to the left.
- This means $ x \leq -2 $

✔ Answer: $ x \leq -2 $

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6)
- Open circle at -1, open circle at 2, shaded between them.
- This means $ -1 < x < 2 $

✔ Answer: $ -1 < x < 2 $

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7)
- Open circle at -2, closed circle at 1, shaded between them.
- This means $ -2 < x \leq 1 $

✔ Answer: $ -2 < x \leq 1 $

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8)
- Open circle at -4, open circle at 2, shaded between them.
- This means $ -4 < x < 2 $

✔ Answer: $ -4 < x < 2 $

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9)
- Closed circles at -3 and 2, shaded between them.
- This means $ -3 \leq x \leq 2 $

✔ Answer: $ -3 \leq x \leq 2 $

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10)
- Open circle at -2, closed circle at 1, shaded between them.
- This means $ -2 < x \leq 1 $

✔ Answer: $ -2 < x \leq 1 $

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✔ Section A Answers Summary:

1) $ x \geq 1 $
2) $ x < 3 $
3) $ x > -1 $
4) $ x \geq -3 $
5) $ x \leq -2 $
6) $ -1 < x < 2 $
7) $ -2 < x \leq 1 $
8) $ -4 < x < 2 $
9) $ -3 \leq x \leq 2 $
10) $ -2 < x \leq 1 $

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Section B: Represent each inequality on the given number lines

Now we graph each inequality.

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1) $ x \geq -2 $
- Draw a closed circle at -2
- Shade to the right

✔ Graph: ●———→ from -2 onward

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2) $ x < 8 $
- Draw an open circle at 8
- Shade to the left

✔ Graph: ←———○ at 8

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3) $ x \leq 5 $
- Draw a closed circle at 5
- Shade to the left

✔ Graph: ←———● at 5

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4) $ x < -3 $
- Draw an open circle at -3
- Shade to the left

✔ Graph: ←———○ at -3

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5) $ x > 6 $
- Draw an open circle at 6
- Shade to the right

✔ Graph: ○———→ from 6 onward

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6) $ 0 < x < 5 $
- Open circles at 0 and 5
- Shade between them

✔ Graph: ○———● (between 0 and 5)

Wait — no: both are open, so:

○———○ (from just above 0 to just below 5)

✔ Graph: open circle at 0, open circle at 5, shaded in between

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7) $ 2 < x \leq 3 $
- Open circle at 2
- Closed circle at 3
- Shade between

✔ Graph: ○———● from 2 to 3

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8) $ 7 < x < 10 $
- Open circles at 7 and 10
- Shade between

✔ Graph: ○———○ from 7 to 10

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9) $ -3 \leq x \leq 2 $
- Closed circles at -3 and 2
- Shade between

✔ Graph: ●———● from -3 to 2

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10) $ -1 < x \leq 4 $
- Open circle at -1
- Closed circle at 4
- Shade between

✔ Graph: ○———● from -1 to 4

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✔ Section B: Instructions for Graphing

For each number line, draw:
- Closed circle (●) for ≤ or ≥
- Open circle (○) for < or >
- Shade the region that satisfies the inequality

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Final Answer Summary:

#### Section A: Inequalities from Number Lines
1) $ x \geq 1 $
2) $ x < 3 $
3) $ x > -1 $
4) $ x \geq -3 $
5) $ x \leq -2 $
6) $ -1 < x < 2 $
7) $ -2 < x \leq 1 $
8) $ -4 < x < 2 $
9) $ -3 \leq x \leq 2 $
10) $ -2 < x \leq 1 $

#### Section B: Graphs of Inequalities
1) $ x \geq -2 $ → ●———→ at -2
2) $ x < 8 $ → ←———○ at 8
3) $ x \leq 5 $ → ←———● at 5
4) $ x < -3 $ → ←———○ at -3
5) $ x > 6 $ → ○———→ at 6
6) $ 0 < x < 5 $ → ○———○ from 0 to 5
7) $ 2 < x \leq 3 $ → ○———● from 2 to 3
8) $ 7 < x < 10 $ → ○———○ from 7 to 10
9) $ -3 \leq x \leq 2 $ → ●———● from -3 to 2
10) $ -1 < x \leq 4 $ → ○———● from -1 to 4

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