need help with easy absolute value question! URGENT (1 Viewer)

[RG11]

5x-7/x <= 4

im getting x<0 and x>=7

sry to ask this stupid q :/

 

[Kurosaki]

its 0<=x<=7 I think. Multiply both sides by x^2, so that the sign doesn't change, and draw a quick graph to see which x-values correspond to y-values

 

[Indoz]

so ... wheres the absolute value?

 

[HeroicPandas]

^Above graph is y = x(x-7)

We want x(x-7) <= 0

Which means we pick x-values that give negative y-values when subbed in the curve ( i have indicated the negative sign in the graph)

 

[RG11]

so ... wheres the absolute value?

lol sry meant unknown in denominator, but was doing absolute value questions hence i got confused.

 

[RG11]

ok so this is how i did it:

5x-7/x <= 4 multiply both sides by x^2

(5x-7)x <= 4x^2

0<=(4x^2)-(5x-7)x

0<=(x)(4x-5x+7)

(x)(4x-5x+7) => 0

(x)(-x+7) => 0

hence since x not equal to 0

solution: x<0 and x=>7


edit: crap, didn't realise that it was a negative parabola so you guys are right.

solution is 0<x<=7

 

[RG11]

thanks alot guys