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# Linear  inequalities

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.

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

1. The distance between two villages is over 18km. write this as an inequality statement.
2. I have x naira, I spend N20, the amount I have left is less than N5. Write inequality in x.
3. The area of a square is less than 25cm2. What can be said about
4. 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 a2 < 25

a <   25,   a < 5

(4) perimeter = 4a since a = 4

then 4a < 4 x 5

4a < 20

a < 5cm

EVALUATION

1. Write the inequality symbols places of the statements below:
2. The car use more than 28 litres of petrol.
3. The cost of the stamp was less than N25.
4. The students got over 60% in the exam.
5. A boy saved over N500. His father gave him N200, the boy now had altogether. Write an inequality in y.
6. The perimeter of a square is less than 28cm what can be said about:
7. 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

1. 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

1. Write an inequality in terms of the unknown.
1. The number of goals n was five or more.
2. the temperature tc was not greater than 38oC.
3. the number of students n was less than 36
4. 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

1. Say whether each of the following statement is true or false?
2. -20 is greater than – 5.
3. -3 x ( -2) > – 3 – 6
4. -18 <3 – 20
5. Illustrate the following on a number line
6. x > 0 b. x ≤ – 1                     c. x  ≥  -2

REVISION QUESTION

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

1. The inequality symbol for -1 is greater than -5 is  (A) – 1 < 5 (B) -5 > -1    (C) -1 > -5
2. The time for a journey t mins was over 2hrs the inequality statement is ……………… (A) t > 2hts B. 2hts > t   C. t  >  2hrs
3. 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

1. ( -3)2 $\left[\right]$ 22

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

THEORY

1. A square has an area of more than 36cm2. What can be said about the length of one of its sides?
2. Sketch the following inequality on a graph.

(A) x ≤ – b                       b.   x ≥ 3.

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