Problem Solving

Hi,

I have this as an inequality:

a/b > b/c

Mathematically, can we cross multiply to make it ac > b^2 ??

Yes you can.

Yes you can provided both b and c are positive.

If atleast one of them is negative , the sign of inequality will change.

pesfunk wrote:Hi,

I have this as an inequality:

a/b > b/c

Mathematically, can we cross multiply to make it ac > b^2 ??

Hi,

you have to be very careful when manipulating inequalities that involve variables.

Remember, when you multiply or divide both sides by a negative, you have to swap the inequality. Since we don't know the sign of b or c, it's NOT safe to cross multiply.

Let's pick numbers to illustrate the danger:

a/b > b/c

if a=4, b=2 and c=-2, our original inequality holds, since:

4/2 > 2/-2
2 > -1

However, if we cross multiply as you suggested:

ac > b^2
(4)(-2) > 2^2
-8 > 4

which most certainly isn't true.

Consequently, you cannot simply cross-multiply (or divide) inequalities by variables with unknown signs.