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Objectives

To enable students to know how to define linear equations. To help students solve simple linear equations. To give students understanding of the concept of worded problems involving linear equations.

Introduction

In general linear equations are found in most calculations in science.In chemistry for example,linear equations are used in balancing chemical equations.In physics newton's laws of motion are mostly linear equations.

Definiton

A linear equation is defined as an equation where the highest power of the unknown is one.

Examples

1. x+2=7
2. 3x-5=3
3. x=8

In all the above examples the highest power of x is one

Solving simple linear equations

To solve simple linear equations the following points should be noted;

1. the sign of any term changes when it is moved from either side of the equal sign to the other e.g from the left-handside{L.H.S}to the right-handside{R.H.S}or vice visa.
2. Any operation you do to the left,you must do to the right,this is because the equation will change otherwise.

Example1

Solve the equation x+3=4

Solution

since x is on the left-handside of the equal sign ,we simply move 3 to the other side of the equal sign giving; x = 4-3 therefore x = 1 is the answer.

Activity

solve the equation

5 - x = 14

Example2

Solve the equation 2x+2=6

Solution

First we move 2 to the right of the equal sign which gives 2x=6-2 this gives us 2x=4; since we are solving for x, we divide both sides of the equal equal sign by 2 thus: 2x/2 = 4/2 by cancellation on both sides we get x = 2

Activity

solve the equation

6 - 3x = 7

Example3

Solve the equation 3x-3=x+7

Solution

Since we have terms in x on both sides of the equation, we collect like terms together ;this gives 3x - x = 7 + 3 therefore 2x = 10 hence x = 5

Activity

find the value of x in the equation

6x - 8 = 5 - 2x

Equations containing brackets

Example4

Solve 2(x - 3) = 6 -3(x - 2)

solution

we first open the bracket

2x - 6 = 6 - 3x + 6

we collect like terms

2x + 3x = 6 + 6 + 6

5x = 18

we divide both sides by 5

x = 18/5 ans

example 5

Solve the equation -2(2x-3) -5 = 9(x-2)

solution

we open the brackets

-4x + 6 -5 = 9x - 18

we collect like terms

9x + 4x = 18 + 6 - 5

15x = 19

x = 19/15 ans