Question

I need to find all the real numbers for
(2x-1)/(4+x) <= 2

Answer 1

what I tried was to move the 2 so that I would get (2x-1)/(4+x)-2 <= 0
and from there I got -9/(4+x) <=0

Answer 2

\[\frac{2x-1}{4+x} \le 2\]Step 1: multiply both sides by 4+x. What do you get?

Answer 3

yea, I'm pretty sure that I'm not allowed to do that

Answer 4

Awww... It seems like...... I'm on the wrong track...

Answer 5

@invidos so because there are x on denominator my opinion that in the first step you need make the restriction for what value not can getting newer x

can you do it ?

Answer 6

x != -4

Answer 7

yes x not can being never equal -4 so because do you can tel me now why ?

Answer 8

because you cannot divide by zero and 4+(-4) = 0
or am I missunderstanding you'r question?

Answer 9

yes do you know it right but with ,,mathanswer" so because than this fraction will be undefined

ok ?

Answer 10

yea

Answer 11

so now can you continue it ?

Answer 12

ehm, so I should just multiply both sides and than say that it is undefined when x =-4?

Answer 13

yes but this x not can being equal -4 this wann being just the first step when you need to solve inequality like in this case

ok ?

so than now you can continue it how you have wrote little up @RolyPoly

Answer 14

Nope, the 2x cancels out on both sides!

Answer 15

x=-4 is a ''critical point'' When x> -4, this inequality is true. When x<-4, this inequality is not true.

Answer 16

ehm, I am feeling kind of slow right now, but when multiplying both sides with (4+x) you get -1<=8
that might be true but it doesn't give anything

Answer 17

ok, but isn't there a "smart" way to solve that?
I undestand how you got that x>-4 but it seems like you just tested you way there

Answer 18

Because I don't think you can 'solve' it using 'normal' way...

Answer 19

so what will get you if you add to both sides (-2) ?

Answer 20

2x-1-8-2x <= 0 if you then multiply both sides with 4+x

Answer 21

the 2x still cancels out!

Answer 22

I guess that you could rewrite everything as (-9)/(4+x) <= 0
which would make it alot easier to se that it cant be smaller than -4

Answer 23

You guys are smart :D