BASIC SIGNS AND PROPERTIES OF LINEAR INEQUALITIES.

**SUBJECT: MATHEMATICS**

**CLASS: JSS 2**

**DATE:**

**TERM: 2nd TERM**

WEEK THREE

**TOPIC: BASIC SIGNS AND PROPERTIES OF LINEAR INEQUALITIES.**

**CONTENT **

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

**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.

**Worked Examples**

- Write the inequality symbols for the following
- b is greater than 15
- 9 x 3 20

2

- ( - 5)2 indicate < or > in the box

Solution

1a. b > 15

- 9 x 3 20.

- (-2)2 = - 2 x 2 = 4

( -5)2 = -5 x -5 = 25

( -2) 2 ( -5)2

**Evaluation**

Write the inequality symbol for each of the following :

- -3 less than + 3
- y is less than – 2
- 4 is greater than a
- ( -5)2 ( 22) 2
- 13 3 x 49

**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 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 **

- x > 18
- I spent N20 out of x naira

Amount left = N(x – 20 )

Less than N5 N(x – 20 ) < N5 i.e

X – 20 < 5

- let the length be a , then a2 < 25

a < 25, a < 5

- 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 liters 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 exceeds 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 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 **

- Note books cost N60 each Deborah has d naira it is not enough to buy a note book. Taiwo has t naira. He is able

to buy a note book. 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 38oC.
- 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?

**GRAPH OF INEQUALITIES**

Consider the number line below:

-4 -3 -2 -1 0 +1 +2 +3 + 4

The inequality graph indicates an arrow head on a number line which show whether the values of x are greater than or less than a given value .

For **Example**:

(a) if x < 2, the inequality graph should show this

x < 2

2 -1 0 1 2 3

(b) if x >, -1, the inequality graph should show this

-2 -1 0 1 2 3

Note: included value ( ¸or > ) makes use of a close circle, ( * ) while not included value ( < or > ) makes use of an open circle ( o)

**EVALUATION **

- Write down the inequality shown in the following graphs.

a).

b). x

8

c). x

-3 -2 -1

**GENERAL EVALUATION **

- Say whether each of the following statement is true or false?
- -20 is greater than Â 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**

- 1
**.**If x is a positive integer positive integer,for what range of values of x is 8 + 2x < 14.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

**WEEKEND ASSIGNMENT**

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

-2 -1 0 1 2 ½ 3 4 5

- n > 2 ½ B. x < 2 ½ C x < -2 ½
- ( -3)2 22

The inequality symbol in the box is

- < B. > C. ≥
- The cost of a stamp #x was not more than N20
- x > N20 B. x = N20 C. x < N20

**THEORY**

- A square has an area of more than 36cm2. What can be said about the length of one of its sides.
- the perimeter.
- Sketch the following inequality on a graph.
- x ≤ - b b. x ≥ 3.

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