algebra next steps we need to get the by itself on one side of the equation multiples of a single...
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Algebra
Next Steps
We need to get the by itself on one side of the equation
Multiples of a Single Variable
Example 1 : Twice Something plus eight equals fourteen
2x
2 8 14x
What is stopping the being by itself at the moment?
2x
The is stopping the being by itself on the left hand side of the equation.
2x
2 148x
8
So how can we get rid of the 8 ?
Take it away !
What we do to one side of the equation, we must do to the other side to keep the equation balanced.
8 2 14 x
Take eight away from the 2x
- 8
=
=
2x
14
- 8 Subtract eight from the 14
Not Balanced !
Balanced !
=2x 6
So x = 3
We need to get the by itself on one side of the equation
Example 2 : Twice something minus eight equals fourteen
2x
2 8 14x
What is stopping the being by itself at the moment?
2x
The is stopping the being by itself on the left hand side of the equation.
2x
2 148x
8
So how can we get rid of the -8 ?
Add eight !!-8 + 8 = 0
= 482 1 xAdd eight to the 2x
+ 8
=2x
14
Not Balanced !
Add eight to the 14
+ 8
=2x
So x = 11
22
Balanced ! But two lots of x !
2 22
22
211
x
x
x
Recap
2x + 7 = 5
2x + 0 = - 2
-2 x = Divide both sides by 2
2
-7
x =
- 7
-1
1.Get rid of hangers
on ! This is an add, so
subtract the
number !2.Now
split the letter from
thegroup
This is times by a number,
so divide by that
number !
Recap
x + 7 = 5
2
x + 0 = - 2
2 x = - 2 2 Multiply both sides by 2
x
-7
= 4
- 7
-
1.Get rid of hangers
on !
This is an add, so
subtract the
number !2.Now split the
letter from the
group
This is divided by a number, so multiply
by that number !
Recap1.Get rid of
hangers on !
Do the opposite to what you see
If the number is positive, subtract it!
If the number is negative, add it!
2.Now split the letter from the
groupIf the letter is is divided by a number, multiply
by that number !
If the letter is is multiplied by a number, divide by that number !
Example 3 : 5 8 14 2x x
Firstly, we must collect the like terms
This means that we need to gather all the letters to one side of the equation.
So we must subtract 2x from both sides of the equation.
2 2 Subtract 2 from both sides
5 8 14 2
3 8
4
1
x x
x
x
x x
3 8 14
3 0 6
3
6
6 Divide both sides by 3
3
8 8 Subtract 6 from both sides
2
x
x
x
x
x
The 8 is stopping the 3x being by itself on the left hand side of the
equation.
We need to get the x by itself on one side of the equation
3 1 8 4x
Do you understand ?
• Push the red button for no
• Push the amber button for maybe.
• Push the green button for yes
Quick Test
For each of the following questions, do the working on a piece of paper and then click on the button nearest to your
answer
24x
2 5 19x 17x
14x 7x
Bad Luck2 5 19
2 0 14
2 14
14 Divide both sides by 2
2
- 5 -5 Subtract 5 from both sid
es
7
x
x
x
x
x
Well Done !!!!
2 5 19
2 0 14
2 14
14 Divide both sides by 2
2
- 5 -5 Subtract 5 from both sid
es
7
x
x
x
x
x
Quick Test- Question 2
Do the working on a piece of paper and then click on the button nearest to your answer
7x
7 7 42x 5x
49x 35x
Bad Luck7 7 42
7 0 49
7 49
49
+ 7 +7 Add 7
to both sid
Divide both sides by 77
s
7
e
x
x
x
x
x
Well Done !!!!
7 7 42
7 0 49
7 49
49
+ 7 +7 Add 7
to both sid
Divide both sides by 77
s
7
e
x
x
x
x
x
Quick Test- Question 3
Do the working on a piece of paper and then click on the button nearest to your answer
47x
5 6 42 2x x 16x
49x 17x
Bad Luck
+ 6 + 6 Add 6 to each si
-2 - 2
d
Subtract 2 from ea
5 6 42 2
3 6 42
3 0 48
3 48
48
ch
Divide both sides by 33
16
side
e
x x
x x
x
x
x
x
x
x
Well Done !!!!
+ 6 + 6 Add 6 to each s
-2 - 2
5 6 42 2
3 6 42
3 0 48
3 48
Subtract 2 from
48 Divide both sides by 3
3
each side
ide
16
x x
x
x
x
x
x x
x
x
Quick Test- Question 4
Do the working on a piece of paper and then click on the button nearest to your answer
74x
5 422
x
47x
26x 23x
Bad Luck
-5 -5 Subtract 5 from each side
5 422
0 372
372
2 = 74 Multiply each side by 22
2 74 Cancel 2
74
x
x
x
x
x
x
Well Done !!!!
-5 -5 Subtract 5 from each side
5 422
0 372
372
2 = 74 Multiply each side by 22
2 74 Cancel 2
74
x
x
x
x
x
x
Congratulations
• You are now ready to try the next stage
Algebra
Intermediate
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