# LINEAR INEQUALITIES

BEHAVIOURAL OBJECTIVE(S): At the ends of the lesson, the students should be able to:

(1) Use the inequality symbols;

(2) Write and interpret linear inequalities in one variable!

(3) Solve linear inequalities in one variable.

PREVIOUS KNOWLEDGE: The students have been introduced to linear algebra in their previous lesson.

REFERENCE(S):  New general Mathematics for junior secondary schools by MF Macrae,  AO Kalejaiye chapter 22 pages 196-204 and  MAN Mathematics for junior secondary schools chapter 11 pages 116 – 119.

TEACHING METHODS: The teacher makes use of discussion method and questioning method.

PRESENTATION: The teacher explains to the students by taking the following steps.

STEP 1: The teacher revises the previous lesson with the students.

STEP 2: The teacher make use of inequality symbols

STEP 3: The teacher write and interpret linear inequalities in one variable

STEP 4: The teacher solve linear inequalities in one variable

CONTENT(S)                                                                     LINEAR INEQUALITIES

In solving mathematical problems, we always use the equal sign, =, more often than any other signs or symbols. For example, 5 + 3 = 8 is a simple equality.

However, when quantities are not equal, they are written 5 + 5 ≠ 8.

Where ≠ means is not equal to.

We can also write 5 + 5 > 8

Where > means is greater than.

Similarly, we can write:  3 + 3 < 8.

Where < means is less than.

=, <, > are inequality symbols.

Note

= means equal to (you are familiar with)

< means less than

> means greater than

Class activity 1: Re-write each of the following using either > or <

• 5 is less than 8
• -1 is greater than -3
• M is greater than 5

Class activity 2: State which statement is true and which is false

• -1 <  -3
• -2 > -3 -4

Example 1: I have x naira. I spend N200. The amount I have left is less than N50. Write an inequality in x.

Solution

I have x naira means Nx

I spent N200 out of  Nx means Nx – N200 = N(x – 200)

Less than N50 means N(x – 200) < N50

Example 2: If 3 is subtracted from twice a number (p), the result is greater than 15.

Solution

Twice a number p means 2 multiply by p = 2p

Subtracted by three mean 2p -3

The result is greater than 15 means 2p – 3 > 15

ASSIGNMENT: Write an inequality in terms of the given unknown.

• The cost of the food, Nx, was over N500
• The time taken, t min, was under 5 min.