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Probability is how likely something is to happen, and we sometimes here it called chance. So, the probability of something happening means how likely it is to happen. It can be expressed in two main ways:
1) A probability scale.
A probability scale looks like a number line, with 0 and 1 at either end. The 0 is labelled "Impossible", as there is 0 chance of it happening. The 1 is labelled "Certain", as it will definitly happen. [This is because 1 is the maximum value our probability can take, so all our probabilities must sum to 1]. Half way along the line is labelled "Even", which means there is an equal chance of the event either happening or not happening [think of tossing a two-sided coin!]. At a quarter is "Unlikely", and three quarters is "Likely". These are used to help position events when they are not impossible/certain, but not evens.
2) A Fraction or a Decimal.
I'll demonstrate this by example. Let's think of an ordinary, fair 6-sided die [Are fair and unbiased the same?]. When I roll this die, the outcomes I could get are "1,2,3,4,5,6". The event which would have probability 1, which I could say is certain of happening, is that "I roll a number". Next I could ask "What fraction of the possible outcomes is greater than 3?", which would be 1/2, because the only outcomes greater than 3 are "4,5,6", which is half of the possible outcomes I could get. So, because probability is how likely something is to happen, I could say "The probability of rolling a number greater than 3 is 1/2".
The definition of the probability of an event is in the form of a fraction, and it is given by:
Probability of an event = (Number of successful outcomes)/(Total number of outcomes)
[Can you see from the definition why our probabilities can't be bigger than 1? Hint: Can the number of successful outcomes be bigger than the total outcomes?]

First, the denominator of the fraction is 2, so all the terms on both sides of the = have to be multiplied by 2:
4x - 6 = 1
Then you can simplify this by adding 6 to both sides:
4x = 7
And then divide both sides by 4:
x = 7/4
x = 1 3/4

5x + 2 = 9
Bring all the numbers which do not include x to the right hand side.
5x = 9 - 2
5x = 7
Now, to find x, 7 should be divided by 5.
x = 7 / 5

Rearrange the equation so x^2 - 7x -18 = 0, then simplify into (x-9)(x+2)=0
-> x=9 or x=-2

Answered by James S.

Studies Financial mathematics at Lancaster

The question is asking you to find the value of x, x represents a number. Therefore, 7x means 7 times a number- this the number we are trying to find out. The first step is to get all the numbers containing an x on one side and the numbers on there own on the other side. To move -20 over you would do the opposite function by adding 20. You would also do this for the +3x by taking away 3x. Now you have your terms separated. As 7 and 3 both contain an x you can minus 3x from 7x, the x stays there as you do not know what this equals yet. You can then add 4 and 20. This gives you 4x=24. This tells you that a number times by 4 equals 24. The number of times 4 goes into 24 is the value of x.

Answered by Rebecca T.

Studies Biology at Nottingham

The equation of the area of a circle is
A = pi*(r^2)
Therefore seeing as we have got the area we must work backwards to be able to answer this question.
First we shall start off with substituting into the equation the numbers that we do know.
9pi= pi*(r^2)
The next step is to get all of the integers on to the same side
9pi/pi=r^2
9=r^2
Continue solving, making sure that what you do to one side you do to the other.
3cm=r

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