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Represent Inequalities on a Number Line

Using a Number Line to Represent Inequalities

The easiest way to represent inequalities is by using a number line. Underneath you can see six in equalities plotted on a number line.
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1. The first inequality is x<2. There is a dot on the two that is not filled in to show that it is not equal to 2. The arrow going down the number line shows that x is any number smaller than 2. 2. The second inequality is x>-3. This time we again have the dot which is not filled in and an arrow going up the number line to show that x is greater than -3. 3. The third inequality is x≤6. The dot is filled in this time showing that x can be equal to 6 and the arrow going down the number line shows that it can also be smaller than 6. 4. The fourth inequality is x≥1. The dot is filled in again since x can also be equal to one. The line going up the number line tells us that x can also be greater than 1. 5. The fifth inequality is -3≤x<7. There are two dots (the one above -3 is filled in since x can be equal to -3 but the one above the 7 is not since x is smaller than 7. The line connecting the two dots tells us that x can also be equal to any number in-between these two dots. 6. The sixth inequality is -4≤x≤1. This time both dots are filled in showing us that x can be equal to -4 and 1. The line connecting the points tells us that x can also be equal to any number in-between -4 and 1. As you may have already realised, there are two different types of dots. The coloured in dot means that the number is smaller/greater or equal to x and the dot that is not coloured in stands for smaller or greater. Always remember to use the right dots when plotting inequalities on a number line

Representing Inequalities as Regions

Using a number line to represent inequalities is easy and effective but using regions to represent them demonstrates more advanced maths skills. Try to represent inequalities as regions next. Please share this page if you like it or found it helpful!
Represent Inequalities as Regions
18.0 INEQUALITIES 18.2 REPRESENTING INEQUALITIES AS REGIONS
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Chapter 18.1:  Learning Outcomes Learn how to use a number line to represent inequalities!

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