Equation thats driving me insane!
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Equation thats driving me insane!
Evening all,
I have begun my studies for the ATPLs with BGS and am going through their maths & physics premodule before starting with the official subjects. So far, I've recapped factors (HCF, LCM), long division and multiplication and shape properties without issue, but one question on formula rearranging is really getting me down because I just can't understand it!
The question is transpose y=7-2x to make x the subject - should be straightforward enough right?
As I understand, the first figure to the right of the = sign will be a positive unless otherwise indicated, so my first step would be to get rid of this (7-7 = 0). Doing the same to the other side, the first issue appears, is it y-7 or 7-y and why?
Secondly, Now being left with -2x is also confusing me. To balance this back to x, are we dividing by -2, resulting in (y-7 or 7-y)/-2 = x? The answer doesn't think so and neither do I, but not sure why
It's only this one question that seems to be catching me out so far and its driving me insane! Rearranging the C=(5(F-32))/9 formula to make F the subject was straightforward compared to this easy question!!?
Hoping not to fall at this first hurdle and that someone can assist in making me feel not quite so stupid!
I have begun my studies for the ATPLs with BGS and am going through their maths & physics premodule before starting with the official subjects. So far, I've recapped factors (HCF, LCM), long division and multiplication and shape properties without issue, but one question on formula rearranging is really getting me down because I just can't understand it!
The question is transpose y=7-2x to make x the subject - should be straightforward enough right?
As I understand, the first figure to the right of the = sign will be a positive unless otherwise indicated, so my first step would be to get rid of this (7-7 = 0). Doing the same to the other side, the first issue appears, is it y-7 or 7-y and why?
Secondly, Now being left with -2x is also confusing me. To balance this back to x, are we dividing by -2, resulting in (y-7 or 7-y)/-2 = x? The answer doesn't think so and neither do I, but not sure why
It's only this one question that seems to be catching me out so far and its driving me insane! Rearranging the C=(5(F-32))/9 formula to make F the subject was straightforward compared to this easy question!!?
Hoping not to fall at this first hurdle and that someone can assist in making me feel not quite so stupid!
My 14 yr old son tells me:
y=7-2x
Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
7-2x=y
Since 7 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 7 from both sides.
-2x=-7+y
Move all terms not containing x to the right-hand side of the equation.
-2x=y-7
Divide each term in the equation by -2.
-(2x)/(-2)=(y)/(-2)-(7)/(-2)
Simplify the left-hand side of the equation by canceling the common factors.
x=(y)/(-2)-(7)/(-2)
Simplify the right-hand side of the equation by simplifying each term.
x=(-y+7)/(2)
y=7-2x
Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
7-2x=y
Since 7 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 7 from both sides.
-2x=-7+y
Move all terms not containing x to the right-hand side of the equation.
-2x=y-7
Divide each term in the equation by -2.
-(2x)/(-2)=(y)/(-2)-(7)/(-2)
Simplify the left-hand side of the equation by canceling the common factors.
x=(y)/(-2)-(7)/(-2)
Simplify the right-hand side of the equation by simplifying each term.
x=(-y+7)/(2)
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Start by transposing the X and Y.
therefore y=7-2x becomes
2x = 7 -y
(change the side, transpose the sign)
Then divide the result by 2 so it becomes
x = (7-y)/2
To confirm this, you can also check the result by using figures, for example I will consider x to be 2 such that 7 - 2X gives me a positive number. Based on this,
y = 7 - ( 2 x 2)
therefore
y=3
Now, I need a formula which, starting with 7, leads me with an answer 2.
So, if I subtract 3 from 7 and divide the answer by 2, I get the desired result.....
x = (7-y)/2
therefore y=7-2x becomes
2x = 7 -y
(change the side, transpose the sign)
Then divide the result by 2 so it becomes
x = (7-y)/2
To confirm this, you can also check the result by using figures, for example I will consider x to be 2 such that 7 - 2X gives me a positive number. Based on this,
y = 7 - ( 2 x 2)
therefore
y=3
Now, I need a formula which, starting with 7, leads me with an answer 2.
So, if I subtract 3 from 7 and divide the answer by 2, I get the desired result.....
x = (7-y)/2
Last edited by Steve6443; 21st Apr 2016 at 19:20.
That is the level of algebra I was taught at the age of 10!
No reflection on the original poster, but just what the hell are schools teaching these days?
No reflection on the original poster, but just what the hell are schools teaching these days?
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G
I retired from teaching in Scotland 10 years ago, and last taught maths in 1972, but would have been surprised if a reasonable 13 year old in one of my science classes had a problem with that. And very surprised if a senior pupil didn't do it automatically.
Think of it as a old of scales or a balance beam.
The equals sign means each side is the same. Then whatever you do to one side do the same to the other, ie subtract or add 7, divide each side by 2 etc until you have whats you want on one side which will equal the remainder on the other side.
Ie y= 7-2x
Add 2x to each side
Gets you y+ 2x = 7
Take y from each side
Gets you 2x =7-y
Divide each side by 2
Gets you x= 7-y / 2
( that is 7-y all divided by 2 )
.
The equals sign means each side is the same. Then whatever you do to one side do the same to the other, ie subtract or add 7, divide each side by 2 etc until you have whats you want on one side which will equal the remainder on the other side.
Ie y= 7-2x
Add 2x to each side
Gets you y+ 2x = 7
Take y from each side
Gets you 2x =7-y
Divide each side by 2
Gets you x= 7-y / 2
( that is 7-y all divided by 2 )
.
Last edited by bingofuel; 21st Apr 2016 at 21:09. Reason: To add the working
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Thank you for your help Thomas coupling, Steve6443 and bingofuel. You have cleared that one up and I will continue with the studies.
To the other posters, though I understand the thoughts on the expected level of maths, I haven't been in a position to use it since leaving school and am doing what I can to refamiliarise myself before starting the first module, hence not just skipping though but taking the time to ask for support on forums like this.
The PPL level of studies at no point required rearranging formulas so it's an area I'm spending a long time in to become accustomed to again.
To the other posters, though I understand the thoughts on the expected level of maths, I haven't been in a position to use it since leaving school and am doing what I can to refamiliarise myself before starting the first module, hence not just skipping though but taking the time to ask for support on forums like this.
The PPL level of studies at no point required rearranging formulas so it's an area I'm spending a long time in to become accustomed to again.
You're 23 - only 7 years out of compulsory education. But yes, were probably handicapped by the paucity of an education system teaching to the test, than teaching for understanding of the subject. That is deeply regrettable, but not your fault - the whole community of STEM professions is seeing this problem (and, for all I know, other fields as well.)
I was sorting out my technical college notes from the 1980s last week - came across a load of notes in my own handwriting on the use of Laplace transforms to solve 2nd order differential equations. They scared me!
Very seriously - if you're struggling at this point, you really do need to go back to the books and refresh GCSE maths, or you'll just keep struggling. Don't just look for patches on specific points - get yourself properly up to speed on the subject generally (ditto basic physics), you'll thank yourself later for the effort.
G
I was sorting out my technical college notes from the 1980s last week - came across a load of notes in my own handwriting on the use of Laplace transforms to solve 2nd order differential equations. They scared me!
Very seriously - if you're struggling at this point, you really do need to go back to the books and refresh GCSE maths, or you'll just keep struggling. Don't just look for patches on specific points - get yourself properly up to speed on the subject generally (ditto basic physics), you'll thank yourself later for the effort.
G
Last edited by Genghis the Engineer; 21st Apr 2016 at 22:20.
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The equals sign means they are equal. So if you do the same to both sides they stay equal and to stay equal that's all you can do. So assaid, add 2x to both sides and subtract y from both sides. Then divide both sides by 2.
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You will soon learn that the BGS material is FULL of mistakes!
But then again so are the ACTUAL EXAMS where you have to chose the WRONG ANSWER in order to get the mark correct for that question.
There are some questions in both the BGS learning materials, the BGS Question Bank and the actual exams that are basic maths - and they get the answer wrong.
Thus is the current state of the EASA ATPL exams, and thus the training for them - unfit for purpose.
But then again so are the ACTUAL EXAMS where you have to chose the WRONG ANSWER in order to get the mark correct for that question.
There are some questions in both the BGS learning materials, the BGS Question Bank and the actual exams that are basic maths - and they get the answer wrong.
Thus is the current state of the EASA ATPL exams, and thus the training for them - unfit for purpose.
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This is true ... but it isn't always obvious which bits you can forget. I never expected to make real life use of having learned how to calculate the transitive closure of a sparse connectivity matrix ... but one day I did just that.
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On formula for convert C to F or F to C note -40c/f are both the same temperature so by referencing back to -40 then the formula becomes ((f+40)x5/9)-40=c and ((c+40)x9/5)-40=f so it is the same basic formula just 5/9 or 9/5 changes so no worry about to add or subtract the 32.
