0
$\begingroup$

I'm trying to solve the following expression for variable $S$ and having some difficulty manipulating the expression because of some negative terms. I have that

$$QS(1+\frac{x_2}{S})+\frac{2y_2}{S}<QS(1+\frac{x_1}{S})+\frac{2y_1}{S}$$

where $Q<0$ and all other variables are positive. $x_2>x_1$ and $y_2>y_1$


My attempt is as follows:

$$QS+Qx_2+\frac{2y_2}{S}<QS+Qx_1+\frac{2y_1}{S}$$

$$\iff Q(x_2-x_1)<\frac{2}{S}(y_1-y_2)$$

multiplying this by $-1$ gives:

$$Q(x_1-x_2)>\frac{2}{S}(y_2-y_1) \iff \frac{Q(x_1-x_2)}{2(y_2-y_1)}>\frac{1}{S} \iff \frac{(y_2-y_1)}{Q(x_1-x_2)}<S$$

Is this correct?

$\endgroup$
1
$\begingroup$

Your work is correct, if it is clear to you that the manipulations at the end work because $Q(x_1-x_2)>0$.

$\endgroup$
1
$\begingroup$

it is correct because division by $y_2-y_1$ does not change the sign since $y_2>y_1$ by assumption.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.