Mathematics/equation help

[NDA]

I have been struggling to help my daughter find a way of solving a group of equations.... for example:

4p - 7 = 5 + 3p

and

7x + 3 = 5 + 5x

There are a whole bundle more, what we're trying to find out is the method of solving them rather than going through every number in the known universe and then experimenting.

Would a clever person be able to help?

Thanks....

[TheEnd]

4p - 7 = 5 + 3p

if you take away 3p from each side you get=

1p - 7 = 5

add 7 to each side

1p = 12

just add or subtract the same numbers on each side of the equals sign

[NDA]

My daughter says "I love you". She's only 12, so let's not go too far at this stage.

Just going to work through this.

Many thanks.

[43034]

Another method, which I was taught in school is:

4p - 7 = 5 + 3p

Group the same letters to one side, so:

4p - 3p = 5 + 7

Which thus equals:

1p = 12.

Remember, if you chance side, you change signs.

[Sticklebrick]

Yeah, what he said. As a general approach it is all about making what you are trying to find , the 'unknown variable' i.e. 'p', the 'subject' of the equation. This means making it into the form:

p = ......

To do this you can do any number of operations but you must do them both sides of the 'equals' sign. Things such as adding or subtracting any given number and multiplying or dividing by any given number. Such as The End has done above to get 'p' as the 'subject' and the equation in the form:

1p = p = .....

Hope this helps.

[NDA]

We're sitting in the garden going through all these at the moment - suffice to say that she's changed her opinion of PH being a bunch of 'sad old losers' to being quite the most sparkling group of highly intellectual, helpful and interesting types!

Excellent stuff, thank you all.....

[Sticklebrick]

No problem, goodluck to her with it all!

[NDA]

TheEnd said:

4p - 7 = 5 + 3p

if you take away 3p from each side you get=

1p - 7 = 5

add 7 to each side

1p = 12

just add or subtract the same numbers on each side of the equals sign

OK, used this and solved the bulk of them. However we're stuck on one:

3n + 8 = 6 - n

We couldn't seem to find a way around this one.

[TheEnd]

NDA said:

OK, used this and solved the bulk of them. However we're stuck on one:

3n + 8 = 6 - n

We couldn't seem to find a way around this one.

add 1n to each side=

4n+8 = 6

so
edit- take away 8 from each side

4n = -2

1n = -0.5

Edited by TheEnd on Saturday 24th April 18:30

[NDA]

Legend.

She is extremely grateful (as am I), we spent such a long while trying to do these - many many thanks!