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Was this set by a teacher, or are you just curious?
3(x+456)+5(56x-45)=0
Multiply out: 3x+3 * 456 + 5 * 56x + 5 *(-45)=0 (i am using * to mean multiply, so it doesn't look like x)
Simplify: 3x + 1368 + 280x -225 = 0
Simplify More: 283x + 1143 = 0
Rearrange (subtract 1143 from both sides): 283x = -1143
Rearrange (divide both sides by 283): x = -1143/283
So, x = -1143/283 = -4.04
But before we all think that Algebra is odd, there IS a mistake in the proof.
When I first saw it I was confooosed, and someone had to point out to me that because we said that a=b, then (a-b) must equal zero. When you start multiplying or dividing by zero, all hell breaks loose, and you start to get weird looking proofs.
So watch out for those in your proofs!
Bit of a puzzle, that one ...
I think we can tease apart the first two terms "16y^2-25x^2"
(4y-5x)(4y+5x) = 4y(4y+5x) -5x(4y+5x) = 16y^2 + 20xy -20xy -25x^2 = 16y^2 -25x^2
But we also need "+10x-1" ...
... making it (4y-5x+2)(4y+5x) adds 8y+10x, so we need to wipe another -8y-1
What does (4y-5x+1)(4y+5x-1) get?
(4y-5x+1)(4y+5x-1) = 4y(4y+5x-1) -5x(4y+5x-1) +1(4y+5x-1) = 16y^2 + 20xy - 4y - 20xy -25x^2 +5x + 4y +5x -1
= 16y^2 -25x^2 +5x +5x -1 = 16y^2 -25x^2 +10x -1
It's a miracle ! I got it by a bit of lucky guessing! (unless I made a mistake)
Yep, because figuring out those sort of puzzles needs logical thinking.
So long as there is a solution available somewhere (just a matter of honor that every puzzle has to be solvable!)
That's great ... let's see some, then.
Congrats!
If they are good ones, sure!
We will help all we can ... just ask a question and someone will answer.
Congratulations! You inspire us to do more.
Ahhh, thank you so much
You noticed, and were curious about, the algebra. You write well, too.
Thank you !
You're doing well!
But there is this one:
Start with: a = b
Then add (-b+b) to the left hand side (this is OK because you are adding 0: a - b + b = b
Now divide both sides by (a-b) and we have:
a - b + b = b
________ _____
(a-b) (a-b)
Reducing the left side:
1 + b = b
____ _____
(a-b) (a-b)
Then subtract b/(a-b) from both sides and you have:
1=0
(Mwuuhahhah - maniacal laughter!)
I know there IS something like this, but right at the start your tutor's proof says "2x=x" which can't be true (unless x=0 when lots of silly things become true).
Depends on where you live. Some countries start Calculus in the final year of high school.
But usually Universities teach it in the first year.
I was thinking of putting a small introduction to it on this website.
Well, I guess I like it all, except proofs. Proofs are just way too strict.
I like the way Algebra can solve problems that normal thinking can't
The difficult kind ! It has calculus in it.
Great! What are your favourite areas?
Feel free to tell us what it is you need help with - if it isn't on the website, we will put it together.
Well, that would work, YiAnZ, if we are allowed to do rounding.
Are we, Steve123? And were you giving us a clue by saying it might be a logic problem? Is there a trick here?
I can get (8-3)*3+8 = 23 ...
And with an extra 3 I can get (3+3)*8/3+8=24
With some logic I could ignore a 3 and 8, and just use 3*8=24
Welcome, Jill. That is a GREAT life.
Sorry, Jack, 8+8+3+3 = 22
30? You sound like 12! I won at Connect 4 just once.
If only there were a better way to test math skills. Exams are so stressful.
Why not get a few old exam papers, and have someone supervise you like a real exam. "It is 9 O'Clock, you can now start ... ". Have a big old clock on the wall to further stress you out. If you can pass an old exam this way, then you will have more confidence in the real exam.
Also, exam preparation is important. What I used to do was this: Every day I studied, I would write down important points on a sheet of paper (like "multiplying negatives gives a positive"). Sometimes I would have 2 or 3 pieces of paper that summarised everything I had learned. An hour before the exam I would find a quiet corner and go over my summary sheets until it was all fresh in my mind.
And you know it is hard to be stressed about anything you have confidence in.
Hope this helps.