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.

When we have the symbol < or > inequality in the given question, we have to use open circle.

When 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.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.