Inequalities on a number line

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A number line is representing the numbers on a straight line. On the number line the numbers are written from left to right in an ascending order, smaller on the left and greater on the right. This helps to identify which number is greater and smaller. A number line can be used to represent an inequality. A greater that sign is represent by ‘>‘ and a smaller than sign can be represented by ‘<‘.    In an inequality two sides of the equation are not the same which leads to comparison of greater than or lesser than.            
Example 1: What inequality does the following number line show?

Solution: Given here is a number line. The filled circle includes the number on the number line. An open circle represents not including the number on the number line.
Now the blue underlined line represents a set of points, which can represented as an inequality. For the inequality a variable x can be taken.
Here the shaded line starts from 3 (including 3) and covers all the points less than 3.
So the inequality will be x is lesser than or equal to 3.
Hence the solution is x ≤ 3.
Question: Multiple choice question (Pick the correct option.)
Which of the following point is not included in the following number line?

a)    1                      b) 5                c) 10               d) None of these.
Correct answer: option a.
The inequality covers all point greater than 1.
Hence, the number line represents the inequality x < 1.
The inequality doesn’t include the point 1 as it has an open circle.

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