**Graph a Linear Inequality in One Variable :**

To graph a linear inequality in one variable, first we have to draw a number line.

Now we have to draw a arrow to represent the given inequality.

For example x < 5 means the value of the variable x is lesser than 5. So it may be 4, 3, 2, 1, 0. We have to graph the given linear inequality as follows.

- Whenever we have the symbol " < " or " > " inequality in the given question, we have to use open circle.
- Whenever we have the symbol " ≤ " or " ≥ " inequality in the given question, we have to use closed circle.

**Example 1 :**

Graph the solutions of the inequality x ≥ -2. Check the solutions.

**Solution : **

**Step 1 :**

Draw a closed circle at -2 to show that -3 is a solution.

**Step 2 :**

Shade the number line to the right of -2 to show that numbers greater than -2 are solutions.

(Use a solid circle for an inequality that uses ≥ or ≤)

**Step 3 :**

Check your solution.

Choose a number that is on the shaded section of the number line, such as -1.

Substitute -1 for x.

-1 ≥ -2

-1 is greater than -2, so -1 is a solution.

**Step 4 :**

Let us prove that -2 is a solution of the inequality x ≥ -2.

In the given inequality, plug y = -2.

Then, we have

-2 ≤ -2 ---> (-2 is greater than or equal to -2) ?

Is the answer for the above question is "yes or "no" ?

The answer for the above question is "Yes".

Because, -2 is equal to -2.

Hence, -2 is a solution to the inequality x ≥ -2.

**Example 2 :**

Graph the solutions of the inequality x ≥ 6. Check the solutions.

**Solution : **

**Step 1 :**

Draw a closed circle at 6 to show that 6 is a solution.

**Step 2 :**

Shade the number line to the right of 6 to show that numbers greater than 6 are solutions.

(Use a solid circle for an inequality that uses ≥ or ≤)

**Step 3 :**

Check your solution.

Choose a number that is on the shaded section of the number line, such as 7.

Substitute 7 for x.

7 ≥ 6

7 is greater than 6, so 6 is a solution.

**Step 4 :**

Let us prove that 6 is a solution of the inequality x ≥ 6.

In the given inequality, plug y = 6.

Then, we have

6 ≤ 6 ---> (6 is greater than or equal to 6) ?

Is the answer for the above question is "yes or "no" ?

The answer for the above question is "Yes".

Because, 6 is equal to 6.

Hence, 6 is a solution to the inequality x ≥ 6.

**Example 3 :**

Graph the solutions of the inequality 1 < m. Check the solutions.

**Solution : **

**Step 1 :**

Draw an empty circle at 1 to show that 1 is not a solution.

**Step 2 :**

Shade the number line to the right of 1 to show that numbers greater than 1 are solutions.

(Use an open circle for an inequality that uses > or <)

**Step 3 :**

Check your solution.

Choose a number that is on the shaded section of the number line, such as 2.

Substitute -4 for y.

1 < 2

1 is less than 2, so 2 is a solution.

**Step 4 :**

Let us prove that 1 is not a solution of the inequality 1 < m.

In the given inequality, plug m = 1.

Then, we have

1 < 1 ---> (1 is less than 1) ?

Is the answer for the above question is "yes or "no" ?

The answer for the above question is "No".

Because, 1 is equal to 1.

Hence, 1 is not a solution to the inequality 1 < m.

**Example 4 :**

Graph the solutions of the inequality t ≤ -4. Check the solutions.

**Solution : **

**Step 1 :**

Draw a solid circle at -4 to show that -4 is a solution.

**Step 2 :**

Shade the number line to the left of -4 to show that numbers less than -4 are solutions.

(Use a solid circle for an inequality that uses ≥ or ≤)

**Step 3 :**

Check your solution.

Choose a number that is on the shaded section of the number line, such as -5.

Substitute -5 for t.

-5 ≤ -4

-5 is less than -4, so -5 is a solution.

**Step 4 :**

Let us prove that -4 is a solution of the inequality t ≤ -4.

In the given inequality, plug t = -4.

Then, we have

-4 ≤ -4 ---> (-4 is less than or equal to -4) ?

Is the answer for the above question is "yes or "no" ?

The answer for the above question is "Yes".

Because, -4 is equal to -4.

Hence, -4 is a solution to the inequality t ≤ -4.

After having gone through the stuff given above, we hope that the students would have understood, how to graph linear inequalities in one variable.

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