sir the shortcut is as follows ? divide the diff. in values at the critical pt and the value given by the slope in that segement. if result has – sign move left,if positive move right,is that a right inference?

Kind of, Jaspreet….but it is more intuitive than that with a little practice. Do 4-5 of these and you will get a rough idea of where the minimum will lie…and yes it is sum of, I will correct it.

If the slope is 4 then every unit of movement in x will cause a change of 4 in y. So if we want y to change by 6 (from 12 to 18) then x has to change by 6/4 i.e. 1.5. As I said in an earlier post, I am going to assume that the reader is familiar with slope and so on, that is a can of worms I don’t want to open now – wanted to cover as much as possible of Modulus before CAT gets seriously underway ðŸ™‚

I guess there is a typo in the last quest, for an odd no: of moduli of slope 1, the curve will be minimum at the middle root and for an even no: of moduli of slope 1, the curve will be flat at the middle two roots, right?

and I the curve will be flat at the center for an even no of moduli of “any” but same slope i.e if two moduli both of slope 2 will make a flat graph at center.
Regards
Kartik

we got the different sloped by plotting., so is there any way to find the solution without plotting any graph.. ? when i did this, i got stuck at a point:
put x= – 5, y= 12 and when we keep modulus positive and put y = 18, we get x=6.5 (which is true) but,
when we put x = -2, we get y = 10, so here if we put y = 18 and take all negative modulii, then x doesn’t comes out to be 2 (which should come), so if you have any way to solve without knowing slopes and plotting graph, plz explain?

I always prefer to draw a rough graph. And the slope will be constant only within a region (where the regions are demarcated by the roots of the original mods). So we have to find a separate slope in each region, as each region corresponds to a different line segment. If you pick one point from one region and another from a different region, the slope between them will not match any of the line segments!

I took all the mods positive once and then took all of them negative,found X.and it is same as actual answer.
will this work everytime?
if not,in which cases it shall work?

It will work as long as the solutions are beyond all the roots, I believe (haven’t formally checked, you can try and do so if you like). If a solution lies between 2 of the roots of the individual moduli, I think it would not work. For example try something like |x-10| +|x| + |x+10| = 25.

sir find the *sum of values of x

sir the shortcut is as follows ? divide the diff. in values at the critical pt and the value given by the slope in that segement. if result has – sign move left,if positive move right,is that a right inference?

Kind of, Jaspreet….but it is more intuitive than that with a little practice. Do 4-5 of these and you will get a rough idea of where the minimum will lie…and yes it is sum of, I will correct it.

regards

J

after getting x=-6,2,wy did u add them to get -4.5? if we put -4.5 in the equation,that doesnot add up to 18. please clarify?

Jpblacki, I missed a couple of words in the question – it should have been “sum of roots”. I’ve corrected it now.

regards

J

Sir did not understand, how do we move 1.5 and 2 units???

Is it possible to understand without graph?

Please explain

Thanks

If the slope is 4 then every unit of movement in x will cause a change of 4 in y. So if we want y to change by 6 (from 12 to 18) then x has to change by 6/4 i.e. 1.5. As I said in an earlier post, I am going to assume that the reader is familiar with slope and so on, that is a can of worms I don’t want to open now – wanted to cover as much as possible of Modulus before CAT gets seriously underway ðŸ™‚

regards

J

Dear J,

I guess there is a typo in the last quest, for an odd no: of moduli of slope 1, the curve will be minimum at the middle root and for an even no: of moduli of slope 1, the curve will be flat at the middle two roots, right?

and I the curve will be flat at the center for an even no of moduli of “any” but same slope i.e if two moduli both of slope 2 will make a flat graph at center.

Regards

Kartik

Yes Jan, edited. Sorry for the late reply!

And Kartik, that is perfectly correct, most graphing problems in algebra scale up when multiplied by a constant factor, this is no exception….

regards

J

Sir, will the curve y=|1-x| and y=|x-1| be the same?

Yes, Pranita, they will.

Consider: | x | = | – x | right? So | x – k | = | – (x – k) | = | k – x |

regards

J

we got the different sloped by plotting., so is there any way to find the solution without plotting any graph.. ? when i did this, i got stuck at a point:

put x= – 5, y= 12 and when we keep modulus positive and put y = 18, we get x=6.5 (which is true) but,

when we put x = -2, we get y = 10, so here if we put y = 18 and take all negative modulii, then x doesn’t comes out to be 2 (which should come), so if you have any way to solve without knowing slopes and plotting graph, plz explain?

I always prefer to draw a rough graph. And the slope will be constant only within a region (where the regions are demarcated by the roots of the original mods). So we have to find a separate slope in each region, as each region corresponds to a different line segment. If you pick one point from one region and another from a different region, the slope between them will not match any of the line segments!

regards

J

How did we get the slope as +2 and -2 in the respective regions?

This is the 4th post in the series; I have explained that in the earlier posts. Start from here: https://cat100percentile.com/2013/10/14/modulus-addition-1/ and move onward, hopefully it will be clear.

regards

J

I took all the mods positive once and then took all of them negative,found X.and it is same as actual answer.

will this work everytime?

if not,in which cases it shall work?

It will work as long as the solutions are beyond all the roots, I believe (haven’t formally checked, you can try and do so if you like). If a solution lies between 2 of the roots of the individual moduli, I think it would not work. For example try something like |x-10| +|x| + |x+10| = 25.

regards

J