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Expanding Brackets. 3(a + 5) What does this mean? ‘add five to a then multiply the whole lot by three’ Or ‘three lots of a added to three lots of 5. Expanding Brackets. 3(a + 5). + 5. + 5. a. a. + 5. a. Expanding Brackets. 3(a + 5). + 5. + 5. a. a. + 5. a. 3(a + 5) =. - PowerPoint PPT Presentation
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3(a + 5)What does this mean?
‘add five to a then multiply the whole lot by three’
Or ‘three lots of a added to three lots of 5
Expanding Brackets
3(a + 5)
Expanding Brackets
+ 5
+ 5
+ 5a
a
a
3(a + 5)
Expanding Brackets
+ 5
+ 5
+ 5a
a
a
3(a + 5) =
3(a + 5)
Expanding Brackets
+ 5
+ 5
+ 5a
a
a
3(a + 5) = (3 x a) +
3(a + 5)
Expanding Brackets
+ 5
+ 5
+ 5a
a
a
3(a + 5) = (3 x a) + (3 x 5) =
3(a + 5)
Expanding Brackets
+ 5
+ 5
+ 5a
a
a
3(a + 5) = (3 x a) + (3 x 5) = 3a + 15
Expanding Brackets6(2a + 4)
+ 4
+ 4
+ 4
6(2a + 4) =
+ 4 + 4
+ 4
(6 x 2a) + (6 x 4)= 12a + 24
Example:5(2z – 3)
Each term inside the brackets is multiplied by the number outside the brackets.
Watch out for the signs!
Expanding Brackets
Example:5(2z – 3)
(5 x 2z) + 5 x -3
Expanding Brackets
Example:5(2z – 3)
(5 x 2z) + 5 x - 3
= 10z – 15
Expanding Brackets
Example:2(3p + 4) + 3(4p + 1)
Expanding Brackets
Example:2(3p + 4) + 3(4p + 1)
= (2 x 3p) + (2 x 4)
Expanding Brackets
Example:2(3p + 4) + 3(4p + 1)
= (2 x 3p) + (2 x 4) + (3 x 4p) + (3 x 1)
Expanding Brackets
Example:2(3p + 4) + 3(4p + 1)
= (2 x 3p) + (2 x 4) + (3 x 4p) + (3 x 1)
= 6p + 8
Expanding Brackets
Practice 1: Expand the brackets:
(a) (i) 7(n – 3)
(ii) 4(2x – 3)
(iii) p(q – 2p)
Multiply out: (3)
(a) 5(2y – 3)
(1)(c) x(2x +y)
(2)Lesson
7n - 21
8x -12
pq – 2p²
10y - 15
2x² + xy
Are you ready for the answers ?
Practice 2: Expand and simplify:
(i) 4(x + 5) + 3(x – 7)
(2) (ii) 5(3p + 2) – 2(5p – 3)
(2)
(2)
Lesson
4x + 9 + 3x -21 = 7x - 12
15p + 10 - 10p + 6 = 5p +16
Are you ready for the answers ?
By using substitution answer the following questions:
(i) Work out the value of 2a + ay when a = 5 and y = –3
(2)(ii) Work out the value of 5t² - 7 when t=4
(iii) Work out the value of 5x + 1 when x = –3
(iv) Work out the value of D when: (4)D = ut + 2kt
If u = 5t = 1.2k = –2
(3)Lesson
-5
73
-14
1.2
Are you ready for the answers ?
TOP How much do you know?Solve the following
(i) x + 5 = 16
(ii) 3x + 4 = 19
(2)(b) 6y + 9 = 45
(1)
(c) 2x – 5 = -1 (2)
(d) 4(x + 3) = 20 (1)
(e) 29 = 9x - 7 (1)
(Total 7 marks)
Lesson
x = 11
x = 5
y = 6
x = 2
x = 4
x = 2
Are you ready for the answers ?
Practice 1: Solve:
(a) (i) 4x + 2 = 18
(ii) 8x – 5 = 19
(iii) 7 = 3y - 8
Multiply out the brackets first:
(a) 2(x + 3) = 16
(1)(c) 3(2x – 3) = 9
(2)Lesson
x = 3
y = 5
x = 5
x = 3
x = 4
Are you ready for the answers ?
Practice 2: Solve:
(i) 2x + 3 = x + 7
(2) (ii) 8r + 3 = 5r + 12
(2) (iii) 9x – 14 = 4x + 11
(2)
(iv) 20y – 16 = 18y - 10
(2)
Lesson
x = 4
3r = 9 r = 3
5x = 25 x = 5
2y = 6 y = 3
Are you ready for the answers ?
Crossing the equals sign
When we take a value across the equals sign we change what it was doing to the opposite.
So, if it was + 2 on one side, when we take it to the other it is – 2If we are x 2 on one side, when we take it to the other it is / 2
For example,
x + 5 = 13
x = 13 – 5
x = 8
Using inverse operations to solve equations
Solve the following equations using inverse operations.
5x = 45
x = 45 ÷ 5x = 9
Check:
5 × 9 = 45
17 – x = 6
17 = 6 + x17 – 6 = x
Check:
17 – 11 = 6
11 = xx = 11
We usually write the letter before the equals sign.
Using inverse operations to solve equations
Solve the following equations using inverse operations.
x = 3 × 7x = 21
Check:
3x – 4 = 14
3x = 14 + 43x = 18
Check:
3 × 6 – 4 = 14
x = 18 ÷ 3x = 6
= 3x
7
= 3217
Balancing equations
Constructing an equation
Ben and Lucy have the same number of sweets.
Ben started with 3 packets of sweets and ate 11 sweets. Lucy started with 2 packets of sweets and ate 3 sweets.
How many sweets are there in a packet?
Let’s call the number of sweets in a packet, n.
We can solve this problem by writing the equation:
3n – 11
The number of Ben’s sweets
=
is the same as
the number of Lucy’s sweets.
2n – 3
Solving the equation
Move the unknowns (letter terms) to one side and the numbers to the other
3n – 11 = 2n – 3 Start by writing the equation down.
3n – 2n = –3 + 11
This is the solution.
We can check the solution by substituting it back into the original equation:
3 8 – 11 = 2 8 – 3
3n - 2n – 11 = – 3
n = 8