Maths modulus question

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#1

why does the sign change, why is it -k instead of +k as shown in the question?

thanks for any help

sorry messed up attachments mb mb ignore the chemistry one
Last edited by pondering-soul; 1 week ago
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1 week ago
#2
I think you've messed up your attachments...
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1 week ago
#3

the simplest way is to draw the graph of y = | 2x - 11 |... it is V shaped.

then draw the graph y = 0.5x on top.

now draw other lines parallel to y = 0.5x and see how many times they meet the V shaped graph
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1 week ago
#4
You can also square both sides and turn it into a typical 'set discriminant >0' question.
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1 week ago
#5
(Original post by the bear)

the simplest way is to draw the graph of y = | 2x - 11 |... it is V shaped.

then draw the graph y = 0.5x on top.

now draw other lines parallel to y = 0.5x and see how many times they meet the V shaped graph
This is the best approach, but if you want an answer as quickly as possible:

It's enough to *sketch* the y = |2x-11| and a couple of sample lines y = 0.5x + k; the only thing you really need to "get right" are the coordinates of the point A where y = |2x-11| changes direction and that 2x has a bigger gradient than 0.5x.

It's obvious that the change between "more than one root" and "no roots" occurs when y=0.5x + k goes through A, and it's fairly obvious whether you need k to be bigger or smaller than this critical value.

I really don't like "square the modulus" approaches because they totally fail to scale to more difficult problems.

Edit: (and in case it's not clear, you only need the sketches to justify the answer. It's entirely possible to do the minimal calculations required to solve this mentally and just write down the answer).
Last edited by DFranklin; 1 week ago
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1 week ago
#6
(Original post by DFranklin)
This is the best approach, but if you want an answer as quickly as possible:

It's enough to *sketch* the y = |2x-11| and a couple of sample lines y = 0.5x + k; the only thing you really need to "get right" are the coordinates of the point A where y = |2x-11| changes direction and that 2x has a bigger gradient than 0.5x.

It's obvious that the change between "more than one root" and "no roots" occurs when y=0.5x + k goes through A, and it's fairly obvious whether you need k to be bigger or smaller than this critical value.

I really don't like "square the modulus" approaches because they totally fail to scale to more difficult problems.

Edit: (and in case it's not clear, you only need the sketches to justify the answer. It's entirely possible to do the minimal calculations required to solve this mentally and just write down the answer).
diagrams help in all kinds of math questions
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