Back to: MATHEMATICS SS2

**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

- 3x -10 < 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

$\frac{2}{3}\u20133x\le 2\left(1\u2013x\right)$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.

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

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GLORYSolve 28 -5x < x -4

Class Tutor28-5x < x-4 collect the like term 28+4 < x+5x 32 < 6x Divide through by 6, to get the answer for x 32/6 < 6x/6 Then, x<5.3 I hope you find this easy?