Given a

Question

Given a<0, what is another way of expressing -ax<1? A) x<1/a B) x>1/a C) x<-1/a D) x>-1/a E) x<1

Bunuel · Answer

Since a is negative, then -a is positive, so we can divide the given inequality and keep the sign: x < -1/a.

Answer: C.

philipssonicare · Answer

Bunuel , how is it different to b?

LevanKhukhunashvili · Answer

You multiply only right hand side by -1 change the sign and leave left hand side as is

x<-1/a multiply by -1 is -x>1/a
not
 x >1/a

Bunuel · Answer

B reads:  x > \frac{1}{a} .

The correct answer is  x < -\frac{1}{a} , which can also be written as  -x > \frac{1}{a}  (by multiplying it by -1). As you can see B and C are not identical.

chetan2u · Answer

Two ways.. (I) substitution.... a<0, so let a=-2.. -ax<1...-(-2)x<1....x<\frac{1}{2} Check the choices.. A) x<\frac{1}{a} ..... x<\frac{1}{-2} ...NO B) x>\frac{1}{a} ..... x>\frac{1}{-2} ...NO C) x<\frac{-1}{a} ..... x<\frac{-1}{-2}.....x<\frac{1}{2} ...YES D) x>\frac{-1}{a} ..... x>\frac{-1}{-2}.........x>\frac{1}{2}.. ...NO E) x<1 ..NO C (II) Algebraically a<0...-a>-0....-a>0 Now -ax<1...divide both sides by -a without changing the sign as -a>0 x<\frac{1}{-a} C

redskull1 · Answer

This is question is awesome. It tests our basics thoroughly. You can get it right in 20 secs

Posted from my mobile device

vanshikaamittal · Answer

why is answer A incorrect? -(-a)x<1, gives us ax<1. therefore, x<1/a.

Bunuel · Answer

The fact that  a  is negative does not mean we can simply replace it with -a, because  a  already represents a negative number. So, -ax < 1 does not imply ax < 1.

Next, x < 1/a is incorrect because if a = -1 and x = 1/2, which satisfy -ax < 1, gives (x = 1/2) > (1/a = -1)

Hope that clears things up!

Given a<0, what is another way of expressing -ax<1?

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