Lesson 10: Simple 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
In all the above examples the highest power of x is one
 * 1) x+2=7
 * 2) 3x-5=3
 * 3) x=8

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.

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

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

6x - 8 = 5 - 2x

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