Back to: MATHEMATICS JSS 2
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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
- 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 a2 < 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 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?
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
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 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
- A square has an area of more than 36cm2. 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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