# Lesson Notes By Weeks and Term - Junior Secondary School 2

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

1. Write the inequality symbols for the following
2. b is greater than 15
3. 9 x 3                20

2

1. ( - 5)2 indicate < or > in the box

Solution

1a.      b > 15

1.   9 x 3   20.

1. (-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 :

1. -3 less than + 3
2. y is less than – 2
3. 4 is greater than a
4. ( -5)2   ( 22) 2
5. 13 3 x 49

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

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

1. let the length be a , then a2 < 25

a <   25,   a < 5

1. 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 liters 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

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

1. 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

1. Write an inequality in terms of the unknown.
2. The number of goals n was five or more.
3. the temperature tc, was not greater than 38oC.
4. the number of students n was less than 36
5. 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

1. Write down the inequality shown in the following graphs.

a).

b).           x

8

c).        x

-3     -2    -1

GENERAL EVALUATION

1. Say whether each of the following statement is true or false?
2.   -20 is greater than Â 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. 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.
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 (i) – 1 < 5   ( b) -5 > -1 (c ) -1 > -5
2. The time for a journey  t mins was over 2hrs the inequality statement is ………………
3. t > 2hts     B. 2hts > t        C. t  >  2hrs
4. The graph below represents thus

-2    -1     0    1    2 ½         3    4    5

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

The inequality symbol in the box is

1. <        B. >            C. ≥
2. The cost of a stamp #x  was not more than N20
3. 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. the perimeter.
3. Sketch the following inequality on a graph.
4.   x ≤ - b         b.   x ≥ 3.