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What Is An Equation?
An Equality
Value Left Side = Value Right Side
Solve An Equation
Find The Value Of The Unknown
This Is Often Represented
By The Letter x
The Type Of Equations
Shown On This Page
Are Linear Equations
A linear equation
has an x in it but no x2
It is a straight line on a graph
Other names for 'linear equations'
are 'simple equations'
or 'straight line equations'
What Is An Operation?
Something that we do, such as
add, subtract, multiply or divide
ACTION
Inverse of + is -
x + a - a = x
Inverse of - is +
x - a + a = x
Inverse of × is ÷
x × a ÷ a = x
Inverse of ÷ is ×
x ÷ a × a = x
BALANCE
If we operate on one side
of an equation
then we must do
the same operation
on the other side
of the equation
to keep it in balance
TIDY UP
SORT OUT BOTH SIDES
Work down the columns
on the left hand side
and then the column
on the right hand side
Finally
write the answer
in the form
x = ...
Video Showing The Idea
That Subtracting From
Both Sides Of An Equality
Maintains The Equality
IF a = b
THEN a - c = b - c
Video With Music
Shows a different layout
of the working
but with the same
underlying method
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Algebra - Equations
Type x + a = b
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x Is An Unknown Number
a And b Are Known Numbers
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Method Steps
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| [1] ACTION |
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undo the addition by subtraction |
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| [2] BALANCE |
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subtract same from other side |
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| [3] TIDY UP |
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sort out both sides |
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Example x + 2 = 5
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x | + | 2 | = | 5 | | |
| [1] ACTION |
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undo add 2
by subtract 2 |
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2 | | | | |
| [2] BALANCE |
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subtract 2
from other side |
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- |
2 | |
| [3] TIDY UP |
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sort out
both sides |
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x |
+ |
0 |
= |
3 | | |
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| | x | = | 3 | | |
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Try The Following Question Yourself
Only Use The Hints If You Need To
x + 1 = 6
The Following Question Has Less Detailed Hints
Only Use The Hints If You Need To
x + 3 = 7
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Some Questions For You To Try Without Any Hints
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| Starters |
A Little Harder |
[1] x + 1 = 5
[2] x + 2 = 8
[3] x + 3 = 10
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[1] x + 10 = 40
[2] x + 11 = 30
[3] x + 12 = 20
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You can check your answers
by adding the value that you get for x
to the number on the left hand side of the equation
and seeing if you get the number on the right hand side
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Create Some Questions For Yourself
x + number = higher number
You can check your answers
by adding the value that you get for x
to the number on the left hand side of the equation
and seeing if you get the number on the right hand side
Do You Understand The Method Using
ACTION - BALANCE - TIDY UP
Could You Explain It To Somebody Else?
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If Something Is Not Clear
Then Please Ask A Question
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Go To maths.com Algebra Index
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maths.com Home
Algebra Index
ONE OPERATION EQUATIONS
Often Called One Step Equations
Note that there is more than one step if we show the method
but that only one operation is used
ONE OPERATION EQUATIONS
SECTION 1
The Equation Has ADDITION
So We Need SUBTRACTION
All Answers Positive
Level 1 x + a = b No Check
THE LINKS BELOW
ARE NOT YET WORKING
Level 2 x + a = b With Check
Level 3 a + x = b With Check
Level 4 b = x + a With Check
Level 5 b = a + x With Check
Answers Positive Or Negative
Level 1 x + a = b No Check
Level 2 x + a = b With Check
Level 3 a + x = b With Check
Level 4 b = x + a With Check
Level 5 b = a + x With Check
WIMS Unlimited Practice
ONE OPERATION EQUATIONS
SECTION 2
The Equation Has SUBTRACTION
So We Need ADDITION
All Answers Positive
Level 1 x - a = b No Check
Level 2 x - a = b With Check
Level 3 b = x - a With Check
ONE OPERATION EQUATIONS
SECTION 3
The Equation Has MULTIPLICATION
So We Need DIVISION
All Answers Positive
Level 1 ax = b No Check
Level 2 ax = b With Check
Level 3 b = ax With Check
ONE OPERATION EQUATIONS
SECTION 4
The Equation Has DIVISION
So We Need MULTIPLICATION
All Answers Positive
Level 1 x/a = b No Check
Level 2 x/a = b With Check
Level 3 b = x/a With Check
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