MTH 112 Elementary Functions Chapter 6 Trigonometric Identities, Inverse Functions, and Equations
MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder...
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Transcript of MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder...
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MTH 3-15aMTH 4-15a
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Revision of Level 2 Algebra
Harder Equations
Equations & Equations & InequalitiesInequalities
ww
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srevis
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Equations with Brackets
Equations with Fractions
Solving Inequalities
Harder Fractions
![Page 2: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/2.jpg)
MTH 3-15aMTH 4-15a
11 Apr 202311 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
![Page 3: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/3.jpg)
MTH 3-15aMTH 4-15a
11 Apr 202311 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
![Page 4: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/4.jpg)
MTH 3-15aMTH 4-15a
11 Apr 2011 Apr 202323
Created by Mr Lafferty Maths DeptCreated by Mr Lafferty Maths Dept
Balancing MethodBalancing Methodw
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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 ?
![Page 5: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/5.jpg)
MTH 3-15aMTH 4-15a
11 Apr 2011 Apr 202323
Created by Mr Lafferty Maths DeptCreated by Mr Lafferty Maths Dept
Balancing MethodBalancing Methodw
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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
![Page 6: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/6.jpg)
MTH 3-15aMTH 4-15a
11 Apr 2011 Apr 202323
Created by Mr Lafferty Maths DeptCreated by Mr Lafferty Maths Dept
Balancing MethodBalancing Methodw
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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
![Page 7: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/7.jpg)
MTH 3-15aMTH 4-15a
11 Apr 2011 Apr 202323
Created by Mr Lafferty Maths DeptCreated by Mr Lafferty Maths Dept
Balancing MethodBalancing Methodw
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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
![Page 8: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/8.jpg)
MTH 3-15aMTH 4-15a
11 Apr 2011 Apr 202323
Created by Mr Lafferty Maths DeptCreated by Mr Lafferty Maths Dept
Balancing MethodBalancing Methodw
ww
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srevis
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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
![Page 9: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/9.jpg)
MTH 3-15aMTH 4-15a
11 Apr 2011 Apr 202323
Created by Mr Lafferty Maths DeptCreated by Mr Lafferty Maths Dept
Balancing MethodBalancing Methodw
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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.
![Page 10: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/10.jpg)
11 Apr 202311 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
![Page 11: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/11.jpg)
11 Apr 202311 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)
![Page 12: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/12.jpg)
11 Apr 202311 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)
![Page 13: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/13.jpg)
11 Apr 202311 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
![Page 14: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/14.jpg)
MTH 3-15aMTH 4-15a
11 Apr 202311 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
![Page 15: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/15.jpg)
MTH 3-15aMTH 4-15a
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
w.m
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srevis
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.com Learning IntentionLearning Intention Success CriteriaSuccess Criteria
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
![Page 16: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/16.jpg)
Examples
11 Apr 202311 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
![Page 17: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/17.jpg)
11 Apr 202311 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
![Page 18: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/18.jpg)
11 Apr 202311 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
![Page 19: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/19.jpg)
MTH 3-15aMTH 4-15a
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
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srevis
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What is my shape?
3 12. Calculate of
4 8
3. Remove brackets 4(5k - 8)
![Page 20: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/20.jpg)
MTH 3-15aMTH 4-15a
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
w.m
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srevis
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.com Learning IntentionLearning Intention Success CriteriaSuccess Criteria
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
![Page 21: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/21.jpg)
11 Apr 202311 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
![Page 22: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/22.jpg)
11 Apr 202311 Apr 2023
Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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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 !
![Page 23: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/23.jpg)
11 Apr 202311 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
![Page 24: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/24.jpg)
MTH 3-15aMTH 4-15a
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
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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
![Page 25: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/25.jpg)
MTH 3-15aMTH 4-15a
11 Apr 202311 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
![Page 26: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/26.jpg)
11 Apr 202311 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
![Page 27: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/27.jpg)
11 Apr 202311 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
![Page 28: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/28.jpg)
11 Apr 202311 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
![Page 29: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/29.jpg)
MTH 3-15aMTH 4-15a
11 Apr 202311 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
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MTH 3-15aMTH 4-15a
11 Apr 202311 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
![Page 31: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/31.jpg)
11 Apr 202311 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 !
![Page 32: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/32.jpg)
11 Apr 202311 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
(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
![Page 33: MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities .](https://reader038.fdocuments.in/reader038/viewer/2022110116/551a1e64550346862c8b4641/html5/thumbnails/33.jpg)
11 Apr 202311 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
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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)
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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
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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
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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
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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
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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
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Now try Exercise 6Ch43 (page 177)
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Solving Inequalities
Equations & Equations & InequalitiesInequalities
MTH 3-15aMTH 4-15a