# Thread: Builder notation - describe complete solution set

1. ## Builder notation - describe complete solution set

Hello Guys first I want to thank the very smart people in here. I only wish you guys could be live to show me how to do some of this stuff.

5/4 (x-1/2) - 5/3 <4/3

{X/X __ __}

Please show me how to do this problem. Thank you very much.

2. Originally Posted by OneidaFL
Hello Guys first I want to thank the very smart people in here. I only wish you guys could be live to show me how to do some of this stuff.

5/4 (x-1/2) - 5/3 <4/3

{X/X __ __}

Please show me how to do this problem. Thank you very much.
At the moment this is unreadable.

I can't tell if the inequality is

$\frac{5}{4}\left(x - \frac{1}{2}\right) - \frac{5}{3} < \frac{4}{3}$

or

$\frac{5}{4\left(x - \frac{1}{2}\right)} - \frac{5}{3} < \frac{4}{3}$.

Please use brackets where they're needed or else learn LaTeX typesetting.

3. Hi, OneidaFL!

I guess it's this:::

$\displaystyle{\frac{5}{4} \left(x - \frac{1}{2}\right) - \left(\frac{5}{3}\right) < \frac{4}{3} }$

$[calculate-the-lowest-common-multiple-(LCM) = 12]$

$\displaystyle{\frac{ 15 (12x - 6) - 20}{12} < \frac{16}{12} }$

$['cut'-the-equal-denominators-and-make-the-count!]$

$15 (12x - 6) - 20 < 16$

$180x - 90 - 20 < 16$

$180x < 16 + 90 + 20$

$180x < 126$

$x < \displaystyle{\frac{126}{180}}$

$x < \displaystyle{\frac{7}{10}}$

PS: I just didn't understand what's:::
{X/X __ __}
IF it's

$\displaystyle{\frac{x}{x} } = 1$

$because$

$x < \displaystyle{\frac{7}{10}}$

$\displaystyle{\frac{7}{10}} : \displaystyle{\frac{7}{10}} = \displaystyle{\frac{70}{70}} \Rightarrow 1$

Hope It helps!

4. Originally Posted by Prove It
Please use brackets where they're needed or else learn LaTeX typesetting.
I Agree!!! =D You should try to learn it! I'ts not so difficult, and It'll help you to find the results here!

5. ## Thank You so very much

Not only did you give me an answer, but you are so specific on showing me the details, that I know get it on how to do the fractions on these problems.