Back to: MATHEMATICS JSS 2

**Welcome to Class !!**

*We are eager to have you join us !!*

*In today’s Mathematics class, We will be discussing Linear Inequalities. We hope you enjoy the class!*

**CONTENT **

- Greater than and less than
- Properties of linear inequalities
- Not greater than and not less than
- Graphs of inequalities.

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**Greater than and less than**

5 + 3 = 8 means equal to

X = 0 means x is not equal to 0

But 5 + 5 > 8, where 7 means greater than

Similarly, 3 x 2 < 8 where < means less than, > and < are inequality symbols.

**READING ASSIGNMENT**

New General Mathematics UBE Edition, Chapter 22, pgs 209-211

Essential Mathematics by A. JS. Oluwasanmi Chapter 23 pgs 237-239

Properties of a linear inequality. The symbol > and < can be used to change word statements into algebraic statements.** **

**Worked Examples**

- The distance between two villages is over 18km. write this as an inequality statement.
- I have x naira, I spend N20, the amount I have left is less than N5. Write inequality in x.
- The area of a square is less than 25cm2. What can be said about
- the length of its sides b. its perimeters

**Solution **

(1) x > 18

(2) I spent N20 out of x naira

Amount left = N(x – 20)

Less than N5 N(x – 20 ) < N5 i.e. X – 20 < 5

(3) let the length be a , then a^{2} < 25

a < 25, a < 5

(4) perimeter = 4a since a = 4

then 4a < 4 x 5

4a < 20

a < 5cm

**EVALUATION **

- Write the inequality symbols places of the statements below:
- The car use more than 28 litres of petrol.
- The cost of the stamp was less than N25.
- The students got over 60% in the exam.
- A boy saved over N500. His father gave him N200, the boy now had altogether. Write an inequality in y.
- The perimeter of a square is less than 28cm what can be said about:
- its length b. its area

** **

**READING ASSIGNMENT **

New General Mathematics UBE Edition, Chapter 22, pgs 213-215

Essential Mathematics by A. JS. Oluwasanmi Chapter 23 pgs 237-239

** **

**NOT GREATER THAN AND NOT LESS THAN**

When a particular variable say x does not exceed a particular value, it means x is not greater than the given value.

For **Example** x __< __ 50, it means x < 50 or x = 50; where __ < __ means less than or equal to. But when the variable x exceeds a given value for **Example** x > 50 or x = 50m it means less than or equal to. But when the variable x exceeds a given value for **Example** x > 50 or x = 50m it means x __> __50 where __> __ means greater than or equal to .

** **

**Worked Examples **

- Notebooks cost N60 each Deborah has d naira it is not enough to buy a notebook. Taiwo has t naira. He is able to buy a notebook. What can be said about the value of d and it?

**Solution **

Deborah = d naira

Deborah amounts is less than N60 d < 60

Taiwo = t naira

In conclusion, t > d and d < t.

__ __

**EVALUATION **

- Write an inequality in terms of the unknown.
- The number of goals n was five or more.
- the temperature tc was not greater than 38
^{o}C. - the number of students n was less than 36
- The pass mark in a test was 27, one person got x marks and failed. Another got y marks and passed, what can be said about x and y?

**GENERAL EVALUATION **

- Say whether each of the following statement is true or false?
- -20 is greater than – 5.
- -3 x ( -2) > – 3 – 6
- -18 <3 – 20
- Illustrate the following on a number line
- x > 0 b. x ≤ – 1 c. x ≥ -2

**REVISION QUESTION**

- If x is a positive integer, for what range of values of x is 8 + 2x < Draw number line to show your answer.
- If x is an integer, find the first three possible values of x in the inequality 6x – 5(x-2) ≤ 4 (2x-1)
- If x is a positive integer and 2x + 3 > -30 + 6p (a) solve for x (b) Find all the possible values of x and show them on a number line.

New General Mathematics UBE Edition, Chapter 22, pgs 213-215

Essential Mathematics by A. JS. Oluwasanmi Chapter 23 pgs 237-239

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**WEEKEND ASSIGNMENT**

- The inequality symbol for -1 is greater than -5 is (A) – 1 < 5 (B) -5 > -1 (C) -1 > -5
- The time for a journey t mins was over 2hrs the inequality statement is ……………… (A) t > 2hts B. 2hts > t C. t
__>__2hrs - The graph below represents thus

-2 -1 0 1 2 ½ 3 4 5

(A) n > 2 ½ B. x < 2 ½ C x < -2 ½

- ( -3)
^{2}$\left[\right]$ 2^{2}

The inequality symbol in the box is (A) < (B.) > C. ≥

5. The cost of a stamp #x was not more than N20 (A) x __> __N20 (B.) x = N20 (C.) x __ < __ N20

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**THEORY**

- A square has an area of more than 36cm
^{2}. What can be said about the length of one of its sides? - Sketch the following inequality on a graph.

(A) x ≤ – b b. x ≥ 3.

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