25-Aug-14Created by Mr. Lafferty Maths Dept. Revision of Level E Algebra Harder Equations Equations & Inequalities Equations with

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


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’.



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



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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



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Revision of Level E


2 3 11x

7x

2 11 3x 4 17 7n 4 7 17n

6n

Examples

2 14x 14 2x 24 4n

4 24n



Now try Exercise 1Ch43 (page 171)

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Revision of Level E




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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


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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



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Harder Equations


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




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Harder Equations




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What is my shape?

3 12. Calculate of

4 8

3. Remove brackets 4(5k - 8)


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1. To show how to solve equations with brackets .

1. Multiply out brackets.

2. Apply ‘change side change sign’ rule.




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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




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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





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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


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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.


2. Apply ‘change side change sign’ rule.



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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




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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





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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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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



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14 6

3

x ( 1)

3 3 4 3 63

x

Examples

1 12 18x 18 13 5x Multiply EVERY

term by 3




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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





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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. 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.




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Inequalities are similar to equations except we replace the “=“ with one of the following symbols :


" <"," >"," "or " "

Less than or

equal to

Greater than or

equal toGreater than

Less than

The Good News



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Solving inequalities is almost identical to solving equations :


2 1 7x 2 7 1x

Example 1

2 8x 4x x is any value less than 4

Even Better News !



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Solving inequalities is almost identical to solving equations :


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


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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

>

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Example 2

5( x – 1 ) - 8x ≥ - 17

5x – 5 – 8x ≥ - 17

- 3x - 5 ≥ - 17

- 3x ≥ - 12

x -12 -3

≤ So x ≤ 4



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Documents

25-Aug-14Created by Mr. Lafferty Maths Dept. Revision of Level E Algebra Harder Equations Equations & Inequalities Equations with