Transcript Word question and answers Booster 13 Level 5 to 6

Booster
Lesson
Lesson 13
Objectives – what you should
be able to do by the end of the
lesson
• Construct simple linear
equations
• Solve simple linear equations
• Check solutions by substituting
John is y years old. Jane is x years old. John is 8
years older than Jane.
Can you write this as an algebraic equation?
y=x+8
In one’s year time, what will John and Jane’s age
be?
Can you write another algebraic equation?
y+1=x+9
Can you add 3 to both sides?
y + 4 = x + 12
Can you take away 4 from both sides?
y=x+8
John is also twice the age of Jane.
Can you write this as an equation?
y = x + 8 = 2x
Solving equations
M13.1
Set 1 1.1
1.2
1.3
1.4
1.5
3x = 13
6C + 8 = 80
18 = 7p - 24
2(n + 4) = 72
4(d - 1) + 3(d + 4) = 57
Set 2 2.1
2.2
2.3
2.4
2.5
9x = 43
7 = 56
a
3x + 6 = 2x + 13
3(x + 2) = 4(x - 1)
x+8
=x-2
2
Set 3 3.1
3.2
3.3
3.4
3.5
7x = -37
3(s - 1) - 2(s - 2) = 0
2(t + 1) - 5(t + 2) = 0
7(h + 3) = 11
7
= 11
x+2
x+5
Set 1
1.1
1.1
1.2
1.3
1.4
1.5
3x = 13
3x = 13
6C + 8 = 80
18 = 7p - 24
2(n + 4) = 72
4(d - 1) + 3(d + 4) = 57
Divide both sides by 3
x = 4.3333…
1.2 6c + 8 = 80
6c = 72
c = 12
Take 8 from both sides
Divide both sides by 6
1.3 18 = 7p - 24
42 = 7p
Add 24 to both sides
Divide both sides by 7
6=p
1.4 2( n + 4) = 72
n + 4 = 36
n = 32
Divide by 2 on both sides
Take 4 from both sides
1.5 4( d – 1 ) + 3 (d + 4) = 57
4d – 4 + 3d + 12 = 57
7d + 8 = 57
7d = 49
d=7
Multiply out brackets
Collect like terms
Take 8
Divide by 7
Set 2
2.1
2.2
2.3
2.4
2.5
2.1 9x = 43
9x = 43
7 = 56
a
3x + 6 = 2x + 13
3(x + 2) = 4(x - 1)
x+8
=x–2
2
Divide both sides by 9
x = 4.7777..
2.2
7 = 56
Multiply both sides by a
a
7a = 56
Divide both sides by 7
a=8
2.3 3x + 6 = 2x + 13
3x = 2x + 7
Take 6 from both sides
Take 2x from both sides
x=7
2.4 3 ( x + 2 ) = 4 ( x – 1)
3x + 6 = 4x - 4
3x = 4x - 10
-x = - 10
2.5
Multiply out brackets
Take 6 from both sides
Take 4x from both sides
x = 10
x+8=x–2
Multiply both sides by 2
2
x + 8 = 2x - 4
Take x from both sides
8=x-4
12 = x
Add 4 to both sides
Set 3
3.1
3.1
3.2
3.3
3.4
3.5
7x = -37
3(s - 1) - 2(s - 2) = 0
2(t + 1) - 5(t + 2) = 0
7(h + 3) = 11
7
= 11
x+2
x+5
Divide both sides by 7
7x = - 37
x = - 5.285…
3.2 3( s – 1 ) – 2 (s – 2 ) = 0
3s – 3 – 2s + 4 = 0
Multiply out brackets
Collect like terms
s + 1 = 0 Take 1 from both sides
s=-1
3.3 2( t+ 1) – 5(t + 2) = 0
2t + 2 – 5t – 10 = 0
- 3t - 8 = 0
- 8 = 3t
Multiply out brackets
Collect like terms
Add 3t to both sides
Divide by 3
- 2.666.. = t
3.4 7( h + 3 ) = 11
Multiply out brackets
Take 21 from both sides
Divide by 7
7h + 21 = 11
7h = - 10
h = - 1.428..
3.5
7
x+2
=
11
x+5
Cross multiply
7( x + 5 ) = 11( x + 2)
7x + 35 = 11x + 22
7x + 13 = 11x
13 = 4x
Multiply out brackets
Take 22
Take 7x
Divide by 4
3.25 = x
A problem to solve:
What is my number?
Multiplying my number by 4 and then subtracting 5
gives the same answer as multiplying my number by 2
and then adding 1.
Use a letter to represent my number and write an equation
4x – 5 = 2x + 1
Add 5 to both sides
Solve the equation.
4x = 2x + 6
2x = 6
Take 2x from both sides
Divide by 2
x=3
Check the solution;
Multiply 3 by 4 then subtract 5 Answer 7
Answer 7
Multiply 3 by 2 and add 1
check
Number puzzles
Two number multiply together to make 24. They
add together to make 11.
What are my numbers? How did you work it out?
Two numbers multiply together to make -15.
They add together to make 2.
What are my numbers? How did you work it out?
Two numbers multiply together to make – 15. They
add together to make – 2.
What are my numbers? How did you work it out?
Two numbers multiply together to make 8. they
add together to make – 6.
What are my numbers? How did you work it
out?
Objectives – how have we
done?
• Construct simple linear
equations
• Solve simple linear equations
• Check solutions by substituting
Thank
you for
your
attention