Inequality Question (1 Viewer)

[~shinigami~]

This question for the 3U Fitzy textbook has really got me stumped. Hope someone can help me

For what values of x is:

(2x-4)/(x+3) > (x+2)/(2x+6)


Thanks in advance.

 

[ssglain]

Have you tried taking out the 2 from the denominator on the LHS, then multiply both sides by (x+3)^2?

 

[rtkl]

so if u follow the instructions from post #2
you should get an answer of

{x: X<-3 union X> 10/3}

i haven t checked this though

 

[bos1234]

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post 2 is the quickets way

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another method but its long.

(2x-4)/(x+3) > (x+2)/(2x+6)
(2x-4)/(x+3) - (x+2)/(2x+6) > 0

(2x-4)/(x+3) - (x+2)/2(x+3) > 0

taking common denom,
[2(2x-4) - (x+2)]/2(x+3)] > 0

Expanding and simplifying,
3x-10/2(x+3) > 0

(3x-10)(x+3)/2 > 0
(3x-10)(x+3) > 0

Draw a quick sketch
y-int = -30
x-int = 10/3 and -3
concave up

x>10/3

or

x<-3

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If you like the case method.

3x-10/2(x+3) > 0

x cannot equal -3

so x > -3 or x < -3

If x > -3
3x-10 > 0
x>10/3

If x < -3
3x-10<0
x<10/3

So x > 10/3 or x < -3

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[~shinigami~]

Thank you so much for the help ssglain, rtkl and bos1234.

I think I've lost all my ability for maths which is bad cause I have my 3 Unit half-yearly tomorrow.