Lesson 10: Simple Linear Equations
Topic 1: Indices and Logarithms  

Indices and Logarithms  Lesson 1: Bases and Indices  Lesson 2: Fractional Indices  Lesson 3: Zero and Negative Indices  Lesson 4: Exponential Equations  Lesson 5: Definition and Laws of Logarithms  Lesson 6: Equations Involving Logarithms  Lesson 7: Introduction to Surds  Lesson 8: Linear Equations  Lesson 9: Simultaneous Equations  Lesson 10: Simple Linear Equations 

Contents
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 greater power of the unknown is one.
Examples
 x+5=12
 5x3=44
 x=9
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;
 the sign of any term changes when it is moved from either side of the equal sign to the other e.g from the lefthandside{L.H.S}to the righthandside{R.H.S}or vice visa.
 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
solve the equation 33x22=44
Solution
since x is on the lefthandside of the equal sign ,we simply move 3 to the other side of the equal sign giving; x = 43 therefore x = 1 is the answer.
5  x = 14
Example2
Solve the equation 2x+2=6
solve the equation 10x22=44
Solution
First we move 2 to the right of the equal sign which gives 2x=62 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 3x3=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
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(2x3) 5 = 9(x2)
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