Algebra

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Algebra

• Equations
• Level 5

Absorb mathematics Solving equations
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A. Look and See

• Each letter in an equation represents an
  unknown number

unknown
3 x 1 10
(3)
A little bit of trial and error might be required
to find a value for x.
Remember 3x means 3 x
I say X is 4 !!
It aint. x is 3 !!
Replace the unknown with the number in brackets.
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A. Look and See

• Each letter in an equation represents an
  unknown number

Both sides of the equal sign are the same.
3 x 1 10
(3)
9 1 10
10 10
No you didnt!
I told you x was 3!
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Class practice.

• Look at the following equations and solve by
  trial and error

5 x 9 31
(8)
40 9 31 31 31
Hint What would you take 9 from to leave 31?
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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( x 2 ) 30
(7)
6 (5) 30 30 30
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Worksheet part A.

• Now attempt questions
• 1, 2, 3, 4, 5, 6, 7 and 8

A calculator might be useful.
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B. 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.
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• Look at the following equation 4 x 7

7
4 x
Expressions
Right Hand Side
Left Hand Side
Think of each equation as a balance.
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IT IS IMPORTANT TO CLEARLY SHOW ALL YOUR WORKING
OUT!
Example
RHS
LHS
- 1
- 1
Remember, the left hand side (LHS) is equal to
the right hand side (RHS).
3 x 1 10
-1 each side
Why both sides?
3 x 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.
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IT IS IMPORTANT TO CLEARLY SHOW ALL YOUR WORKING
OUT!
Example
- 1
- 1
3 x 1 10
-1 each side
Now divide both sides by 3.
3
3
3 each side
3 x 9
3x 3 gt 3x
X 3
3
x
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• 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) !
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• Example

4( x 2 ) 20
- 8
- 8
4x
- 8 each side
8
20
4
4
4 each side
4x 12
x 3
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Worksheet part B.

• Now attempt questions 9, 10, 11, 12 and 13.

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C. Formulae.

• Look at the shape below

Find the value of x if the perimeter is 12 cm.
Perimeter 12 cm.


12
X cm
X
X
X cm
- 6
- 6
2x 6 12
-6 each side
2
2
2x 12
2 each side
x 6 cm
6 cm
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