Inequalities and Their Graphs
A mathematical sentence that uses symbols such as <, ≤, ≠, > or ≥ to compare two quantities is called an inequality. It is a relationship between two numbers or mathematical expressions that are not equal.
![Inequalities and their graph](https://staging.etutorworld.com/wp-content/uploads/2020/07/Inequalities-and-their-graph.png)
Example:
i) x is a real number less than or equal to 5.
x<= 5
![Inequalities and their graph1](https://staging.etutorworld.com/wp-content/uploads/2020/07/Inequalities-and-their-graph1.png)
ii) x is a real number greater than 8.
x > 8
![Inequalities and their graph2](https://staging.etutorworld.com/wp-content/uploads/2020/07/Inequalities-and-their-graph2.png)
![Inequalities and their graph3](https://staging.etutorworld.com/wp-content/uploads/2020/07/Inequalities-and-their-graph3.png)
Example: -3x > 12
Dividing both sides of an inequality by -3, we get
x < -4
Check Point
Graph the following inequalities on a number line:
1) x < -2
2) x >= 6
3) 2x – 1 <=7
4) -3x + 1 <= 16
5) 4x + 3 > x + 24
Answer Key
1) x < -2, start a ray from -2 with an open dot and extend it towards -∞
2) x ≥ 6, start a ray from +6 with a closed dot and extend it towards +∞
3) 2x – 1 <=7
2x ≤ 8
x ≤ 4
4) -3x + 1 <= 16
-3x ≤ 15
Dividing both sides by -3, we have
x ≥ -5
5) 4x + 3 > x + 24
4x – x > 24 – 3
3x > 21
x > 7