Inequalities

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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

$\frac{2}{3}– 3x \le 2\left(1–x\right)$

            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.

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