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18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Revision of Level E Algebra
Harder Equations
Equations & Equations & InequalitiesInequalities
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Equations with Brackets
Equations with Fractions
Solving Inequalities
Harder Fractions
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
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20 4
2. The ratio of apples to pears is 3:1.
I f there are 24 pieces of f ruit in total.
How many apples are there.
x x x x
x
1. Mulitply out and simplify
3. Factorise
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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2.2. Solving simple algebraic Solving simple algebraic equations.equations.
1. To revise Level E using the rule ‘‘change side change change side change sign’.sign’.
Revision of Level E
1.1. Know ruleKnow rule‘‘change side change side
change sign’.change sign’.
Equations & Equations & InequalitiesInequalities
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
We use the rule “change side change sign”
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Revision of Level E
Reminder !
5 11x
16x 11 5x 8 8x
8 8x
0x
Examples
Equations & Equations & InequalitiesInequalities
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Revision of Level E
“Opposite of multiplication is division”
2 12x
6x 12 2x 17 3n
3 17n
253
x
Examples
Equations & Equations & InequalitiesInequalities
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Revision of Level E
We use the rule “change side change sign”
2 3 11x
7x
2 11 3x 4 17 7n 4 7 17n
6n
Examples
2 14x 14 2x 24 4n
4 24n
Equations & Equations & InequalitiesInequalities
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Exercise 1Ch43 (page 171)
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Revision of Level E
Equations & Equations & InequalitiesInequalities
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
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4 ( )2. Expand out the brackets y x y
1. Find the perimeter and area of the shape.
3. Find all the missing angles.
6x
2x
100o
60o
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1.1. Use same rules to solve Use same rules to solve equations with more than equations with more than one x term.one x term.
1. To explain how we use the same rules to solve harder equations were we have more than one x term.
Harder Equations
Equations & Equations & InequalitiesInequalities
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Harder Equations
We use the rule “change side change sign”
Same old Rule !
6 1 2 21x x
5x
6 2 21 1x x
Examples
4 20x 20 4x
10 9 4 30x x
3 13 36 2
x
10 4 30 9x x 6 21x 21 6x
Equations & Equations & InequalitiesInequalities
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Exercise 2Ch43 (page 173)
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Harder Equations
Equations & Equations & InequalitiesInequalities
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
ww
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srevis
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.com 1. I have an infi nite amount of line symmetry.
What is my shape?
3 12. Calculate of
4 8
3. Remove brackets 4(5k - 8)
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1. To show how to solve equations with brackets .
1. Multiply out brackets.
2. Apply ‘change side change sign’ rule.
Equations with Brackets
Equations & Equations & InequalitiesInequalities
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Apply ‘change side change sign’ rule
2(2 3) 24x x 4 6 24x x
Examples
3 18x 18 3 6x
Equations with Brackets
Equations & Equations & InequalitiesInequalities
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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5(3 2) 2(4 3) 2 36x x x 15 10 8 6 2 36x x x
Examples
7 16 2 36x x
20 5 4x
5 16 36x 5 20x
Equations with Brackets
Equations & Equations & InequalitiesInequalities
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Exercise 3Ch43 (page 174)
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Equations with Brackets
Equations & Equations & InequalitiesInequalities
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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7 (3 9 )
51. of 63
7
1 12. Calculate 2 1
2 4
3. Expand the brackets
4. Calculate the area of the shape.
f e f
5cm
11cm
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1. To show how to solve equations that contain fractional terms.
1. Multiply every term to get rid of fractional term.
Equations with Fractions
2. Apply ‘change side change sign’ rule.
Equations & Equations & InequalitiesInequalities
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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.com multiply EVERY term to get rid of fractional term.
and Apply ‘change side change sign’ rule
13 7
2x
12 2 3 2 72x
Examples
6 14x 14 6 8x Multiply EVERY
term by 2
Equations with Fractions
Equations & Equations & InequalitiesInequalities
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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.com multiply EVERY term to get rid of fractional term.
and Apply ‘change side change sign’ rule
3 22
4 3x
3 212 12 12 2
4 3x
Examples
9 8 24x 7
16 9 19
x Multiply EVERY
term by 12
Equations with Fractions
Equations & Equations & InequalitiesInequalities
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Exercise 4Ch43 (page 175)
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Equations with Fractions
Equations & Equations & InequalitiesInequalities
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
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7 14
1. 75% of 160
1 12. Calculate 2 - 1
2 6
3. Factorise
4. Calculate the area of the shape.
f e 7cm
13cm15cm
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1. To show how to solve HARDER fractional equations using all the rules learned so far.
1. Know all rules learned so far.
2. Use these rules to solve harder equations.
Harder Fractional Equations with Brackets
Equations & Equations & InequalitiesInequalities
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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srevis
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.com multiply EVERY term to get rid of fractional term.
and Apply ‘change side change sign’ rule
14 6
3
x ( 1)
3 3 4 3 63
x
Examples
1 12 18x 18 13 5x Multiply EVERY
term by 3
Harder Fractional Equations with Brackets
Equations & Equations & InequalitiesInequalities
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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(2 1) 14 3
x x
3 212 (2 1) 12 12 1
4 3x x
Example
9(2 1) 8 12x x 18 9 8 12x x
Multiply EVERY
term by 12
26 21x 21
26x
Harder Fractional Equations with Brackets
Equations & Equations & InequalitiesInequalities
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Exercise 5Ch43 (page 176)
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Harder Fractional Equations with Brackets
Equations & Equations & InequalitiesInequalities
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
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2 2
1. 5.67 + 2.3 - 0.07
2. Find the highest common f actor f or
(a) 8 and 12 (b) 20x and 48x
3. Calculate 6b + 5a b when a=(-1) b=(-2)
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1. To show how we can solve inequalities using the same rules we use for equations.
1. Understand the term inequality.
2. Solve inequalities using the same method as equations.
Solving Inequalities
Equations & Equations & InequalitiesInequalities
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Inequalities are similar to equations except we replace the “=“ with one of the following symbols :
Solving Inequalities
" <"," >"," "or " "
Less than or
equal to
Greater than or
equal toGreater than
Less than
The Good News
Equations & Equations & InequalitiesInequalities
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Solving inequalities is almost identical to solving equations :
Solving Inequalities
2 1 7x 2 7 1x
Example 1
2 8x 4x x is any value less than 4
Even Better News !
Equations & Equations & InequalitiesInequalities
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Solving inequalities is almost identical to solving equations :
Solving Inequalities
2(2 3) 9x x
4 6 9x x
Example 2
3 6 9x 3 15x
x is any value greater than or equal to 5
15 3x
5x
Equations & Equations & InequalitiesInequalities
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Solving Inequalities
Equations & Equations & InequalitiesInequalities
The only one to watch out for is when you are dividing by a negative
Example
8 – 3m < 2
-3m < -6
m -6 -3
Subtract 8 from each side
Divide across by -3 and change the Sign
So m > 2
>
18 Apr 202318 Apr 2023
Solving Inequalities
Equations & Equations & InequalitiesInequalities
Example 2
5( x – 1 ) - 8x ≥ - 17
5x – 5 – 8x ≥ - 17
- 3x - 5 ≥ - 17
- 3x ≥ - 12
x -12 -3
≤ So x ≤ 4