HOW TO PLOT INEQUALITIES ON A NUMBER LINE

To plot the given inequalities in the number line, we must know the below rules.

1. If we have the inequality

< (less than) or > (greater than),

we have to use the empty / unfilled circle.

2. If we have the inequality sign 

≤ (less than or equal to) or ≥ (greater than or equal to),

we have to use the filled circle.

Also we must know the meaning of two words "And & Or".

Draw a number line graph of:

Problem 1 :

{x│-2 ≤ x ≤ 3}

Solution :

 -2 ≤ x ≤ 3

Since the given inequalities -2 ≤ x ≤ 3 (less than or equal and less than or equal), we draw the line from -2 with a filled circle to 3 with a filled circle on the number line.

Problem 2 :

{x│0 < x < 3}

Solution :

Since the given inequalities 0 < x < 3 (less than and less than), we draw the line from 0 with an unfilled circle to 3 with an unfilled circle on the number line.

Problem 3 :

{x │ x < 1  or x > 3}

Solution :

Given, x < 1 or x > 3 is a compound inequality OR.

Since the first inequality x < 1 (less than), so we draw the line left side from 1 with an unfilled circle on the number line.

Since the second inequality x > 3(greater than), so we draw the line right side from 3 with an unfilled circle on the number line.

Problem 4 :

{x│ x ≤ 2 or x ≥ 3}

Solution :

Given, x ≤ 2 or x ≥ 3 is a compound inequality OR.

Since the first inequality x ≤ 2 (less than or equal), so we draw the line left side from 2 with a filled circle on the number line.

Since the second inequality x ≥ 3(greater than or equal), so we draw the line right side from 3 with a filled circle on the number line.

Problem 5 :

{x│ x ≤ -2 or x > 1}

Solution :

Given, x ≤ -2 or x > 1 is a compound inequality OR.

Since the first inequality x ≤ -2 (less than or equal), so we draw the line left side from 2 with a filled circle on the number line.

Since the second inequality x > 1(greater than), so we draw the line right side from 1 with an unfilled circle on the number line.

Problem 6 :

{x│-1 < x ≤ 4}

Solution :

Since the given inequalities -1 < x ≤ 4 (less than and less than or equal), we draw the line from -1 with an unfilled circle to 4 with a filled circle on the number line.

Problem 7 :

{x│ -3 ≤ x < 0}

Solution :

Problem 8 :

{x│ x < 0 or x ≥ 4}

Solution :

Problem 9 :

{x│ x ≤ -1 or 0 ≤ x ≤ 3}

Solution :

Problem 10 :

{x│ -2 ≤ x ≤ 2 or x ≥ 4}

Solution :