Math Is Fun Forum

Maou-Sama

Member

Registered: 2015-03-03

Posts: 9

inequilities

need help with this ratio inequalities

Last edited by Maou-Sama (2015-03-08 23:15:39)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,134

Re: inequilities

hi Maou-Sama

In most respects inequalities can be treated similarly to equations.  The main exception is what happens if you multiply (or divide) by a negative.  The special rule works like this:

If x > y then -x < -y

If you change the signs on the numbers by multiplying or dividing by a negative, then the inequality must be reversed.  If you're not sure why then think about x and y on a number line and where -x and -y are on the line.

So now to the problem.  You need to multiply both sides by (x-2) and that could be negative.  So consider two cases:

If x-2 > 0  ***

15 > (3x-2)(x-2)

Multiply out the brackets, bring the 15 across and re-factorise so you have 0 > (...)(...)  One of those brackets must be negative and one positive, so take together all three constraints including *** and see what values of x (if any) that gives.

Then repeat with x-2 < 0 and see what values of x that gives.  Think also about whether x can actually be equal to 2.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Olinguito

Member

Registered: 2014-08-12

Posts: 649

Re: inequilities

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either all the factors are positive, or two of them are negative and one positive.

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Bassaricyon neblina