**Graph inequalities on a number line worksheet :**

Here we are going to see some practice questions on graph inequalities on a number line.

(1) Solve the following linear inequality and graph.

2x - 4 ≤ 0

(2) Solve the following linear inequality and graph.

-3x + 12 < 0

(3) Solve the following linear inequality and graph.

4x - 12 ≥ 0

(4) Solve the following linear inequality and graph.

7x + 9 > 30

(5) Solve the following linear inequality and graph.

5x - 3 < 3x + 1

(6) Solve the following linear inequality and graph.

3x + 17 ≤ 2(1 - x)

(7) Solve the following linear inequality and graph.

2(2x + 3) - 10 ≤ 6 (x - 2)

**Question 1 :**

Solve the following linear inequality and graph.

2x - 4 ≤ 0

**Solution :**

**2x - 4 ≤ 0**

**Add 4 on both sides**

**2x - 4 + 4 ****≤ 0 + 4**

**2x ****≤ 4**

**Divide by 2 on both sides**

**2x/2 ****≤ 4/2**

**x ≤ 2**

**Hence, any real number less than or equal to 2 is a solution of the given equation.**

The solution set of the given inequality is (-∞, 2].

**Question 2 :**

Solve the following linear inequality and graph.

-3x + 12 < 0

**Solution :**

-3x + 12 < 0

**Subtract 12 on both sides**

-3x + 12 - 12 < 0 - 12

-3x < -12

Divide by -4 on both sides

-3x/(-3) < -12/(-3)

x < 4

**Hence, any real number less 4 is a solution of the given equation.**

The solution set of the given inequality is (-∞, 2].

**Question 3 :**

Solve the following linear inequality and graph.

4x - 12 ≥ 0

**Solution :**

4x - 12 ≥ 0

**Add 12 on both sides**

4x - 12 + 12 ≥ 0 + 12

4x ≥ 12

Divide by 4 on both sides

4x/4 ≥ 12/4

x ≥ 3

**Hence, any real number greater than or equal to 3 is a solution of the given equation.**

The solution set of the given inequality is [3, ∞).

**Question 4 :**

Solve the following linear inequality and graph.

7x + 9 > 30

**Solution :**

7x + 9 > 30

**Subtract 9 on both sides**

7x + 9 - 9 > 30 - 9

7x > 21

Divide by 7 on both sides

7x/7 > 21/7

x > 3

**Hence, any real number greater than 3 is a solution of the given equation.**

The solution set of the given inequality is (3, ∞).

**Question 5 :**

Solve the following linear inequality and graph.

5x - 3 < 3x + 1

**Solution :**

5x - 3 < 3x + 1

**Subtract 3x on both sides**

**5x - 3 - 3x < 3x + 1 - 3x **

**2x - 3 < 1 **

**Add 3 on both sides**

**2x - 3 + 3 < 1 + 3**

**2x < 4**

**Divide by 2 on both sides**

**2x/2 < 4/2**

**x < 2**

**Hence, any real number lesser than 2 is a solution of the given equation.**

The solution set of the given inequality is (2, ∞).

**Question 6 :**

Solve the following linear inequality and graph.

3x + 17 ≤ 2(1 - x)

**Solution :**

3x + 17 ≤ 2(1 - x)

3x + 17 ≤ 2 - 2x

**Add 2x on both sides**

**3x + 2x + 17 ** ≤ 2 - 2x + 2x

5x + 17 ≤ 2

Subtract 17 on both sides

5x + 17 - 17 ≤ 2 - 17

5x ≤ -15

Divide by 5 on both sides

5x/5 ≤ -15/5

x ≤ -3

**Hence, any real number lesser than or equal to -3 is a solution of the given equation.**

The solution set of the given inequality is (-∞ , -3].

**Question 7 :**

Solve the following linear inequality and graph.

2(2x + 3) - 10 ≤ 6 (x - 2)

**Solution :**

2(2x + 3) - 10 ≤ 6 (x - 2)

4x + 6 - 10 ≤ 6 x - 12

4x - 4 ≤ 6 x - 12

Subtract 6x on both sides

4x - 4 - 6x ≤ 6 x - 12 - 6x

-2x - 4 ≤ - 12

Add 4 on both sides

-2x - 4 + 4 ≤ - 12 + 4

-2x ≤ - 8

Divide by -2 on both sides

-2x / (-2) ≤ - 8 / (-2)

x ≤ 4

**Hence, any real number lesser than or equal to 4 is a solution of the given equation.**

The solution set of the given inequality is (-∞ , 4].

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