Lesson 10: Simple Linear Equations

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


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.


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


  1. x+5=12
  2. 5x-3=44
  3. 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;

  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.


Solve the equation x+3=4

solve the equation 33x-22=44


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.

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solve the equation

5 - x = 14


Solve the equation 2x+2=6

solve the equation 10x-22=44


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

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solve the equation

6 - 3x = 7


Solve the equation 3x-3=x+7


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

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find the value of x in the equation

6x - 8 = 5 - 2x

Equations containing brackets


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


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)


we open the brackets

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

we collect like terms

9x + 4x = 18 + 6 - 5

15x = 19

x = 19/15 ans