Solve and show step by step please? 1.-2/5x - 9 0

Question

Solve and show step by step please?
1.-2/5x - 9 < 9/10
2.q + 12 - 2 (q-22) > 0

austinl · Answer

Ok, let's start with 1 shall we? :)

$\displaystyle -\frac{2}{5}x-9<\frac{9}{10}$

Now, what do you think the first step would be?

austinl · Answer

Hello? @nsnchris 
Any thoughts?

anonymous · Answer

no lol

austinl · Answer

Ok, for the most part, we can treat inequalities like equations. We just have to remember a few rules in doing so.

$\displaystyle-\frac{2}{5}x-9=\frac{9}{10}$

Any thoughts now? What would we do first?

anonymous · Answer

divide each side by - 2/5x

austinl · Answer

That isn't what I would do first. When you have one variable that you are solving for, you want it on one side and constants on the other. In this particular instance, we can simply add 9 to each side.

$\displaystyle -\frac{2}{5}x<\frac{9}{10}+\frac{90}{10}$

Which when simplified is,

$\displaystyle -\frac{2}{5}x<\frac{99}{10}$

Now, what would we do?

anonymous · Answer

now divide it?

austinl · Answer

Yep, and when we divide by a fraction, we have to multiply by its reciprocal.

$\displaystyle(-\frac{5}{2})\times -\frac{2}{5}x<\frac{99}{10}\times(-\frac{5}{2})$

Now, when you multiply or divide an inequality by a negative, you must flip the sign.

$\displaystyle x>\frac{99\times-5}{10\times2}\Leftrightarrow~x>-\frac{495}{20}$

austinl · Answer

Make sense?

anonymous · Answer

kind of lol

austinl · Answer

That should be the answer, as it isn't reduce-able.

anonymous · Answer

yeah thanks