1. ## Help

Could someone help me with this question.

$mx +m^2 > nx + n^2 and m < n, which of the following is true.$

$A) x < m + n$

$B) x > m + n$

$C) x > -m - n$

$D) x < -m - n$

Thank you

2. ## Re: Help

Originally Posted by ridy
Could someone help me with this question.

mx + m^2 > nx + n^2 and m < n, which of the following is true.

A) x > m + n

B) x > m + n

C) x > -m - n

D) x < -m - n

Thank you
Idk if this is right but this is what I got:

$mx +m^2 > nx + n^2$

$mx - nx > n^2 - m^2$

$(m-n)x > (n+m) (n-m)$

$But since m is less than n, therefore, (m-n) is less than 0. This means we must flip the inequality when diving both sides by (m-n)$

$∴ x < (\frac {(n+m) (n-m)} {m-n})$

$x < - (\frac {(n+m) (m-n)} {m-n})$

$x < - (n + m)$

$x < - n - m$

$Therefore, the answer is D$

Idk if did this correctly. Hopefully it's right!

3. ## Re: Help

Originally Posted by captainhelium
Idk if this is right but this is what I got:

$mx +m^2 > nx + n^2$

$mx - nx > n^2 - m^2$

$(m-n)x > (n+m) (n-m)$

$But since m is less than n, therefore, (m-n) is less than 0. This means we must flip the inequality when diving both sides by (m-n)$

$∴ x < (\frac {(n+m) (n-m)} {m-n})$

$x > (\frac {(n+m) (m-n)} {m-n})$

$x > n + m$

$Therefore, the answer is B$

Idk if did this correctly. Hopefully it's right!
Thank you! I'm not sure that is the correct answer, but I'm pretty sure it is. However I am confused at this part of the working out.

$∴ x < (\frac {(n+m) (n-m)} {m-n})$

$x > (\frac {(n+m) (m-n)} {m-n})$

How did the $(n-m)$ change to $(m-n)$?

PS: I did write the solution to A) incorrectly, I have fixed this.

4. ## Re: Help

Originally Posted by ridy
Thank you! I'm not sure that is the correct answer, but I'm pretty sure it is. However I am confused at this part of the working out.

$∴ x < (\frac {(n+m) (n-m)} {m-n})$

$x > (\frac {(n+m) (m-n)} {m-n})$

How did the $(n-m)$ change to $(m-n)$?

PS: I did write the solution to A) incorrectly, I have fixed this.
Oh oops, I forgot to do a certain step (taking the minus sign out). I've edited my last post. Sorry for this! I think it's D instead. Lol I'm kinda prone to silly mistakes.

5. ## Re: Help

Originally Posted by captainhelium
I can second this.

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