Question

How do you write the interval \[\left( { - \infty,2} \right]\] as an inequality involving x and show each inequality using the real number line?

Answer 1

Hint: In this question we are asked to plot on the number line. In order to proceed with this question we need to know what the number line is and how to plot on the number line. A number line is a straight line with numbers placed at equal intervals along its length. A number line can extend till infiniti in any direction and is usually horizontal. An inequality is a relation which makes an unequal comparison between two numbers. It is frequently used to compare two numbers on the number line by their size.

Complete step by step solution:
Given,\[\left( { - \infty,2} \right]\]
Because the right side of the interval is a "]" or bracket, then the inequality contains the value there which is $2$ and so the inequality we right will contain an "or equal to" clause:
$x \leqslant 2$
On the number line the right side of the line representing this interval will be a solid circle indicating the inequality contains an "or equal to" clause:

Note: Brackets play a major role while plotting a number on a number line. “[“ bracket represents that the number is included in the range whereas “(“ bracket represents that the number is not included in the range. When “[“ is used we put a small circle on the number, I number line to represent that the number is included.