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# 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.

Example:

i)      x is a real number less than or equal to 5.

x<= 5

ii) x is a real number greater than 8.

x > 8

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

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

4xx > 24 – 3

3x > 21

x > 7

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