MTH 3-15aMTH 4-15a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Revision of Level 2 Algebra
Harder Equations
Equations & Equations & InequalitiesInequalities
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Equations with Brackets
Equations with Fractions
Solving Inequalities
Harder Fractions
MTH 3-15aMTH 4-15a
21 Apr 202321 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
MTH 3-15aMTH 4-15a
21 Apr 202321 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 2 using the rule
‘‘Balancing Method’Balancing Method’
Revision of Level 2
1.1. Understand the process of Understand the process of thethe
‘‘Balancing Method’Balancing Method’
Equations & Equations & InequalitiesInequalities
MTH 3-15aMTH 4-15a
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4
44
4
Kirsty goes to the shops every week to buy some potatoes. She always buys the same total weight. One week she buys 2 large bags and 1 small bag. The following week she buys 1 large bag and 3 small bags.
If a small bags weighs 4 kgs. How much does a large bag weigh?
What instrument measures balance
How can we go about solving this using balance ?
MTH 3-15aMTH 4-15a
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4 44
4Take a small bag away
from each side.
Take a big bag away from each side.
We can see that a big bag is equal to
4 + 4 =8 kg
MTH 3-15aMTH 4-15a
21 Apr 2021 Apr 202323
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P P4 P
44
4Lets solve it using maths.
Let P be the weigh of a big bag.
We know that a small bag = 4
2P + 4 P + 12
What symbol should we use for
the scales ?
= Subtract 4 from each
side-4 -4
2P=P + 8Subtract P from each
side-P -P
P=8
MTH 3-15aMTH 4-15a
21 Apr 2021 Apr 202323
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Group of 5 adults and 3 children go to the local swimming.Another group of 3 adults and 8 children also go swimming.The total cost for each group is the same. A child’s ticket costs £2.
If a child’s ticket costs £2. How much for an adult ticket ?
a a 2
a 2
a a 2Let a be the price of an adult ticket.
We know that a child price = £2
2 aa
2 a
2 22
2 22
MTH 3-15aMTH 4-15a
21 Apr 2021 Apr 202323
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Balancing MethodBalancing Methodw
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5a + 6 3a + 16=
Subtract 6 from each
side
-6 -6
5a=3a + 10
Subtract 3a from each
side
-3a -3a
2a=10
a a
a
a a
2
2
2
aa
a
2
2
2
2
22
22
Divide each side by 2
a=5
Adult ticket price is £5
1
MTH 3-15aMTH 4-15a
21 Apr 2021 Apr 202323
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It would be far too time consuming to draw out
the balancing scales each time.
We will now review how to use the rules for solving equations.
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
The Balancing Method
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Revision of Level 2
Reminder !
Examples
Equations & Equations & InequalitiesInequalities
MTH 3-15aMTH 4-15a
x – 5 = 11+ 5 + 5
x = 16
x + 8 = 37- 8 - 8
x = 29
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
The Balancing Method
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Revision of Level 2
Reminder !
Examples
Equations & Equations & InequalitiesInequalities
MTH 3-15aMTH 4-15a
6x = 72
x = 12
(÷ 6)
2x = 11
x = 5.5
(÷ 2)
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Revision of Level 2
Examples
Equations & Equations & InequalitiesInequalities
MTH 3-15aMTH 4-15a
4x – 2 = 34+ 2 + 2
4x = 36
x = 9
(÷ 4)
2x + 9 = 31- 9 - 9
2x = 22
x = 11
(÷ 2)
21 Apr 202321 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 2
Equations & Equations & InequalitiesInequalities
MTH 3-15aMTH 4-15a
MTH 3-15aMTH 4-15a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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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
MTH 3-15aMTH 4-15a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1.1. Apply balancing method Apply balancing method to solve equations with to solve equations with more than one x term.more than one x term.
1. We are learning how to apply balancing method to solve harder equations.
Harder Equations
Equations & Equations & InequalitiesInequalities
Examples
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Harder Equations
Equations & Equations & InequalitiesInequalities
MTH 3-15aMTH 4-15a
3x + 2 = x + 10- 2 - 2
3x = x + 8
2x = 8
(÷ 2)
- x - x
x = 4
4x - 5 = 2x - 25+ 5 + 5
4x = 2x – 20
2x = -20
(÷ 2)
- 2x - 2x
x = -10
Each group has 2 minutes come up with a method for solving this type of
equation
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Harder Equations
Equations & Equations & InequalitiesInequalities
MTH 3-15aMTH 4-15a
x + 4 = 3x - 10- 4 - 4x = 3x - 14
3x = x + 14
(÷ 2)
+ 14 + 14
x = 7
Swap Round
!3x - 14 = x
- x - x2x = 14
4x - 1 = 7x + 11+ 1 + 1
4x = 7x + 12
7x = 4x - 12
(÷ 3)
- 12 - 12
x = -4
Swap Round
!7x + 12 = 4x
- 4x - 4x3x = -12
Examples
21 Apr 202321 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
MTH 3-15aMTH 4-15a
MTH 3-15aMTH 4-15a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
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What is my shape?
3 12. Calculate of
4 8
3. Remove brackets 4(5k - 8)
MTH 3-15aMTH 4-15a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1. We are learning how to solve equations with brackets .
1. Remember rule for Multiply out brackets.
2. Apply ‘Balancing Method’ to solve equations.
Equations with Brackets
Equations & Equations & InequalitiesInequalities
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Multiply out the brackets first and then
Balancing Method
Equations with Brackets
Equations & Equations & InequalitiesInequalities
MTH 3-15aMTH 4-15a
3(x – 2) = 33
3x - 6 = 33
3x = 39
+ 6 + 6
x = 13(÷ 3)
Example
Each group has 2 minutes come up with a method for solving this type of
equation
21 Apr 202321 Apr 2023
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Example
Equations with Brackets
Equations & Equations & InequalitiesInequalities
MTH 3-15aMTH 4-15a
5(3x + 2) – 2(4x - 3) = 2x + 36
7x + 16 = 2x + 36- 16 - 167x = 2x + 20- 2x - 2x
5x = 20(÷ 5)
x = 4
15x + 10 – 8x + 6 = 2x + 36Tidy up terms !
21 Apr 202321 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
MTH 3-15aMTH 4-15a
MTH 3-15aMTH 4-15a
21 Apr 202321 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
MTH 3-15aMTH 4-15a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1. We are learning how to solve equations that contain fractional terms.
1. Remember to multiply every term to get rid of fractional term.
Equations with Fractions
2. Apply ‘Balancing Method’
Equations & Equations & InequalitiesInequalities
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Multiply EVERY term to get rid of fractional term.
and then apply ‘Balancing Method’
Equations with Fractions
Equations & Equations & InequalitiesInequalities
MTH 3-15aMTH 4-15a
x + 3 = 712
(x 2)x + 6 = 14
x = 8
- 6 - 6
Each group has 2 minutes come up with a method for solving this type of
equation Example
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Equations with Fractions
Equations & Equations & InequalitiesInequalities
MTH 3-15aMTH 4-15a
x - = 434
(x 4)3x - 2 = 16
3x = 18
+ 2 + 2
12
(÷ 3)
x = 6
Multiply EVERY term to get rid of fractional term.
and then apply ‘Balancing Method’
Example
21 Apr 202321 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
MTH 3-15aMTH 4-15a
MTH 3-15aMTH 4-15a
21 Apr 202321 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
MTH 3-15aMTH 4-15a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1. We are learning how to solve HARDER fractional equations using all the rules learned so far.
1. Apply Balancing Method to solve harder equations.
Harder Fractional Equations with Brackets
Equations & Equations & InequalitiesInequalities
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Harder Fractional Equations with Brackets
Equations & Equations & InequalitiesInequalities
MTH 3-15aMTH 4-15a
+ 5 = 8x + 24
(x 4)
x + 2 + 20 = 32
x + 22 = 32- 22 - 22
x = 10
Multiply EVERY term to get rid of fractional term.
and then apply ‘Balancing Method’
Example
Tidy Up !
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Harder Fractional Equations with Brackets
Equations & Equations & InequalitiesInequalities
MTH 3-15aMTH 4-15a
(x 6)
18x
22x - 36 = 96
(÷ 22)x = 6
(2x – 4) + x = 1632
23
(2x – 4) + x = 969 4
22x = 132
- 36 + 4x = 96
Example
Tidy Up !
+ 36 + 36
21 Apr 202321 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
MTH 3-15aMTH 4-15a
MTH 3-15aMTH 4-15a
21 Apr 202321 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)
MTH 3-15aMTH 4-15a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1. We are learning 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
21 Apr 202321 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
MTH 3-15aMTH 4-15a
MTH 3-15aMTH 4-15a
21 Apr 202321 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
x is any value less than 4
Even Better News !
Equations & Equations & InequalitiesInequalities
Example 2x – 1 < 7+ 1 + 1
2x < 8
x < 4(÷ 2)
NEVER put in an equal sign
MTH 3-15aMTH 4-15a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Solving Inequalities
Equations & Equations & InequalitiesInequalities
Example2(2x – 3) ≥ x + 9
+ 6 + 6
x ≥ 5
NEVER put in an equal sign
4x ≥ x + 9– 6
4x ≥ x + 15- x - x
x is any value greater than or equal to 5
(÷ 3)
3x ≥ 15
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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
MTH 3-15aMTH 4-15a
8 – 3m < 2- 8 - 8
-3m < -6
m > 2(÷ -3) FLIP sign
MTH 3-15aMTH 4-15a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Solving Inequalities
Equations & Equations & InequalitiesInequalities
Example5(x – 1) - 8x ≥ -17
+ 5 + 5
x ≤ 4
5x - 8x ≥ -17– 5
-3x - 5 ≥ -17
x is any value less than or equal to 4
(÷ -3)
-3x ≥ -12
Tidy Up !
FLIP sign
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Exercise 6Ch43 (page 177)
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Solving Inequalities
Equations & Equations & InequalitiesInequalities
MTH 3-15aMTH 4-15a
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