Transcript Equations/ Inequalities

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Equations & Inequalities
Revision of Level E Algebra
Harder Equations
Equations with Brackets
Equations with Fractions
Harder Fractions
Solving Inequalities
31-Mar-17
Created by Mr. Lafferty Maths Dept.
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Starter Questions
1. Mulitply out and simplify 3 x( x  6)  x( x  3)
2. The ratio of apples to pears is 3 :1.
If there are 24 pieces of fruit in total.
How many apples are there.
3.
31-Mar-17
Factorise 20 x  4
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Equations & Inequalities
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Revision of Level E
Learning Intention
1. To revise Level E using the
rule
‘change side change sign’.
Success Criteria
1. Know rule
‘change side change sign’.
2. Solving simple algebraic
equations.
31-Mar-17
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Equations & Inequalities
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Revision of Level E
Reminder !
We use the rule “change side change sign”
Examples
x  5  11
 x  11  5
 x  16
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x 8 8
 x  88
x0
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Equations & Inequalities
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Revision of Level E
Reminder !
“Opposite of multiplication is division”
Examples
2 x  12
 x  12  2
x6
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3n  17
 n  17  3
2
 x5
3
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Equations & Inequalities
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Revision of Level E
Reminder !
We use the rule “change side change sign”
Examples
2 x  3  11
 2 x  11  3
 2 x  14
 x  14  2
x7
31-Mar-17
4n  7  17
 4n  17  7
 4n  24
 n  24  4
n6
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Equations & Inequalities
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Revision of Level E
Now try Exercise 1
Ch43 (page 171)
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Starter Questions
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1.
Find the perimeter and area of the shape.
2x
6x
2. Expand out the brackets
3.
4 y( x  y)
Find all the missing angles.
100
o
60
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o
Equations & Inequalities
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Harder Equations
Learning Intention
1. To explain how we use the
same rules to solve harder
equations were we have
more than one x term.
31-Mar-17
Success Criteria
1. Use same rules to solve
equations with more than one
x term.
Created by Mr. Lafferty Maths Dept.
Equations & Inequalities
Harder Equations
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Same old Rule !
We use the rule “change side change sign”
Examples
6 x  1  2 x  21
 6 x  2 x  21  1
 4 x  20
 x  20  4
 x5
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10 x  9  4 x  30
 10 x  4 x  30  9
 6 x  21
 x  21  6
3
1
 x3 3
6
2
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Equations & Inequalities
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Harder Equations
Now try Exercise 2
Ch43 (page 173)
31-Mar-17
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Starter Questions
1. I have an infinite amount of line symmetry.
What is my shape?
2. Calculate
3
1
of
4
8
3. Remove brackets 4(5k - 8)
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Equations & Inequalities
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Equations with Brackets
Learning Intention
1. To show how to solve
equations with brackets .
31-Mar-17
Success Criteria
1. Multiply out brackets.
2. Apply ‘change side change
sign’ rule.
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Equations & Inequalities
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Equations with Brackets
Multiply out the brackets first
and then
Apply ‘change side change sign’ rule
Examples
2(2 x  3)  x  24
 4 x  6  x  24
 3 x  18
 x  18  3  6
31-Mar-17
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Equations & Inequalities
Equations with Brackets
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Examples
5(3x  2)  2(4 x  3)  2 x  36
 15 x  10  8 x  6  2 x  36
 7 x  16  2 x  36
 5 x  16  36
 5 x  20
 x  20  5  4
31-Mar-17
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Equations & Inequalities
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Equations with Brackets
Now try Exercise 3
Ch43 (page 174)
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Starter Questions
1.
5
of 63
7
2. Calculate 2
1
1
1
2
4
5cm
3. Expand the brackets 7 f (3e  9 f )
4. Calculate the area of the shape.
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11cm
Equations & Inequalities
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Equations with Fractions
Learning Intention
1. To show how to solve
equations that contain
fractional terms.
31-Mar-17
Success Criteria
1. Multiply every term to get
rid of fractional term.
2. Apply ‘change side change
sign’ rule.
Created by Mr. Lafferty Maths Dept.
Equations & Inequalities
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Equations with Fractions
multiply EVERY term to get rid of fractional term.
and
Apply ‘change side change sign’ rule
Examples
1
x3 7
2
1
 2 x  23  2 7
2
 x  6  14  x  14  6  8
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Multiply
EVERY
term by
2
Equations & Inequalities
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Equations with Fractions
multiply EVERY term to get rid of fractional term.
and
Apply ‘change side change sign’ rule
Examples
3
2
3
2
x   2  12  x  12   12  2
4
3
4
3
7 Multiply
 9 x  8  24  x  16  9  1 EVERY
9 term by
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12
Equations & Inequalities
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Equations with Fractions
Now try Exercise 4
Ch43 (page 175)
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Starter Questions
1. 75% of 160
2. Calculate 2
3. Factorise
1
1
-1
2
6
7 f  14e
7cm
4. Calculate the area of the shape.
13cm
31-Mar-17
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15cm
Equations & Inequalities
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Harder Fractional Equations with Brackets
Learning Intention
1. To show how to solve
HARDER fractional
equations using all the
rules learned so far.
31-Mar-17
Success Criteria
1. Know all rules learned so
far.
2. Use these rules to solve
harder equations.
Created by Mr. Lafferty Maths Dept.
Equations & Inequalities
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Harder Fractional Equations with Brackets
multiply EVERY term to get rid of fractional term.
and
Apply ‘change side change sign’ rule
Examples
( x  1)
x 1
 3 4  3 6
 4  6  3
3
3
 x  1  12  18  x  18  13  5Multiply
EVERY
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term by
3
Equations & Inequalities
Harder Fractional Equations with Brackets
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Example
3
2
Multiply
(2 x  1)  x  1
EVERY
term by
4
3
12
3
2
 12  (2 x  1)  12  x  12 1
4
3
 9(2 x  1)  8 x  12  18 x  9  8 x  12
21
 26 x  21  x 
26
31-Mar-17
Created by Mr. Lafferty Maths Dept.
Equations & Inequalities
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Harder Fractional Equations with Brackets
Now try Exercise 5
Ch43 (page 176)
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Created by Mr. Lafferty Maths Dept.
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Starter Questions
1. 5.67 + 2.3 - 0.07
2. Find the highest common factor for
(a) 8 and 12
(b)
20x and 48x
3. Calculate 6b2 + 5a2b when
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a = (-1) b = (-2)
Equations & Inequalities
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Solving Inequalities
Learning Intention
1. To show how we can solve
inequalities using the same
rules we use for equations.
31-Mar-17
Success Criteria
1. Understand the term
inequality.
2. Solve inequalities using
the same method as
equations.
Created by Mr. Lafferty Maths Dept.
Equations & Inequalities
Solving Inequalities
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The Good News
Inequalities are similar to equations except
we replace the “=“ with one of the following symbols :
" < "," > ","  "or "  "
Less than
Greater than
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Less than
or
equal to
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Greater than
or
equal to
Equations & Inequalities
Solving Inequalities
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Even Better News !
Solving inequalities is almost identical to solving equations :
Example 1
2x 1  7
2x  7 1
2x  8
x4
31-Mar-17
x is any value less than 4
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Equations & Inequalities
Solving Inequalities
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Solving inequalities is almost identical to solving equations :
Example 2
2(2 x  3)  x  9
4x  6  x  9
3x  6  9
x  15  3
3 x  15
x  5 x is any value greater than or equal to 5
31-Mar-17
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Equations & Inequalities
Solving Inequalities
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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
Subtract 8 from each side
m > -6 Divide across by -3 and change the Sign
-3
So m > 2
31-Mar-17
Equations & Inequalities
Solving Inequalities
Example 2
5( x – 1 ) - 8x
≥ - 17
5x – 5 – 8x ≥ - 17
- 3x - 5 ≥ - 17
- 3x ≥ - 12
x
31-Mar-17
≤ -12
-3
So x ≤ 4
Equations & Inequalities
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Solving Inequalities
Now try Exercise 6
Ch43 (page 177)
31-Mar-17
Created by Mr. Lafferty Maths Dept.