# Inequalities

Welcome to class!

In today’s class, we will be talking about inequalities. Enjoy the class!

### Inequalities

#### LINEAR INEQUALITIES

There are different signs used in inequalities.

>   Greater than

<    Less than

≥    Greater or equal to

≤  Less or equal to

$\ne$

Not equal to

Example 1: Consider a bus with x people in it.

(a) If there are 40 people then x= 40, this is an equation, not inequality.⁮

(b) If there are less than 30 people on the bus then x   30 where means less than; this is an inequality. It literally means that the number of people on the bus is not up to 30.

Example 2: Find the range of value of x for which

7x – 6 ≥ 15

7x ≥  15 + 6

7 x ≥ 21

x≥ 3

Example 3: Solve the inequality

12x -7 ≥ 13 + 2x

12x-2x ≥ 13+7

10x ≥ 20

x ≥ 2

Evaluation

Solve the inequalities

1. 3x -10 < 2
2. Given that x is an integer, find the three greatest values of x which satisfies the inequality        7x+15 ≥ 2x
##### Inequalities with Reversing Symbols

Anytime an inequality is divided or multiplied by a negative value, the symbol is reversed to satisfy the inequality.

Example

Solve: 14- 2a < 4

– 2a < 4 – 14

– 2a  <  -10

Divide both sides by -2 and reverse the sign (symbols).

a >   5

Check:

If  a > 5,then  possible  values  of  a  are : 6,7,8,…

Substituting, a=6

14  –  2(6)  < 4

14  -12   <   4

2     <   4

Multiply through by 3 or put the like terms together

2-9x ≤ 6(1-x)

2 – 9x ≤ 6-6x

– 9x + 6x ≤ 6-2

– 3x  ≤    4

x  ≥ –  4

3

In our next class, we will be talking about Inequalities in Two Variables.  We hope you enjoyed the class.

Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.