REPRESENTING LINEAR INEQUALITIES ON A NUMBER LINE

To represent 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.

To see more examples

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

To see more examples

Represent the inequalities on a number line :

Example 1 :

x ≤ 7

Solution :

Let us represent the given inequality in the number line.

x ≤ 7

Since the given inequality x ≤ 7 (less than or equal), so we draw the line left side from 7 with a filled circle on the number line.

Example 2 :

x > 8

Solution :

x > 8

Since the given inequality x > 8 (greater than), so we draw the line right side from 8 with an unfilled circle on the number line.

Example 3 :

-8 < x ≤ 10

Solution :

-8 < x ≤ 10

Since the given inequalities -8 < x ≤ 10 (less than and less than or equal), so we draw the line from -8 with an unfilled circle to 10 with a filled circle on the number line.

Example 4 :

x ≥ −1 and x < 4

Solution :

Given, x ≥ −1 and x < 4 is a compound inequality AND.

Since the first inequality x ≥ −1 (greater than or equal), so we draw the line right side from -1 with a filled circle on the number line.

Since the second inequality x < 4 (less than), so we draw the line left side from 4 with an unfilled circle on the number line.

Now, we have to find the overlapping region(intersection).

Example 5 :

x ≤ -2 or x ≥ 0

Solution :

Given, x ≤ -2 or x ≥ 0 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 ≥ 0(greater than or equal), so we draw the line right side from 0 with a filled circle on the number line.

Since we have OR, we combine all the solution of both inequalities.

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