Download Algebra - Every Maths Topic

Algebra
Equations
Absorb mathematics: Solving equations
‘Look and See’
Each letter in an equation represents an ‘unknown’ number:
unknown
3 (3)
x + 1 = 10
Remember 3x means 3 × x
It ain’t. x is
3 !!
A little bit of trial and error
might be required to find a
value for x.
I say X
is 4 !!
Replace the unknown with the
number in brackets.
‘Look and See’
Each letter in an equation represents an ‘unknown’ number:
3 (3)
x + 1 = 10
9 + 1 = 10
Both sides of the
equal sign are the
same.
10 = 10
No you
didn’t!
I told you
x was 3!
Class practice.
Look at the following equations and solve by trial and error:
5 (8)
x – 9 = 31
– 9would
= 31
Hint:40
What
you take 9 from to
leave31
31?= 31
Class practice.
Look at the following equations and solve by trial and error:
Hint: You have to
deal with the
brackets first!
6 times what will
give you 30?
6( (7)
x – 2 ) = 30
6 (5) = 30
30 = 30
Balancing equations.
A calculator might be required.
At some point equations become too difficult to solve by eye.
A method is required to find the unknown value.
Balancing the equation
This is where we treat each
equation like a balanced set of
scales.
 Look at the following equation:
4 + x== 77
Expressions
Left Hand Side
Right Hand Side
Think of each equation as a balance.
IT IS IMPORTANT TO CLEARLY SHOW ALL YOUR
WORKING OUT!
Example:
Remember, the left
hand side (LHS)
is equal to the right
hand side (RHS).
LHS
3x+
RHS
-1
-1
1 = 10 [ -1 each side]
3x=9
Take away 1 from
both sides.
A: The LHS must always equal the RHS.
So whatever is done to one side must be done
on the other side of the equal sign.
Why
both
sides?
IT IS IMPORTANT TO CLEARLY SHOW ALL YOUR
WORKING OUT!
Example:
-1
Now divide both sides
by 3.
3x ÷ 3
=> 3x
3
=x
3 x + 1 = 10
÷3
3x=9
X=3
-1
÷3
[ -1 each side]
[ ÷3 each side]
Example:
keyword
4( x + 2 ) = 20
The LHS is a product, 4 × brackets.
Two choices for first step:
Either a) ÷ 4 both sides.
or b) multiply out brackets.
Lets do
b) !
Example:
4( x + 2 ) = 20
-8
-8
4x + 8 = 20 [- 8 each side]
÷4 ÷4
[÷ 4 each side]
4x = 12
x =3
Formulae.
Look at the shape below:
Find the value of x if the perimeter is 12 cm.
Perimeter = 12 cm.
X cm
X cm
6 cm
+
+
= 12
-6 -6
2x + 6 = 12
[-6 each side]
÷2 ÷2
2x = 12 [÷2 each side]
x = 6 cm