Show that one equation equals another (simple algebra)
I have what appears to be a simple question but am lost as how to start it. I have been asked to show that:
$$\left|\frac{64}{3x-5}-4\right|=\left|\frac{12}{3x-5}\right|\cdot|x-7|$$
Is there some sort of logical process that I can follow in this instance - a process I could put into code for a computer to follow, or do I simply need to have some sort of insight to 'see' what I need to do, because that is something I am really bad at.
Could someone please instruct me on how I should start this, and also let me know what the significance of the absolute brackets are? I find them confusing and don't understand their purpose in this question.
Thank you
$\endgroup$ 11 Answer
$\begingroup$We have
\begin{eqnarray} \left|\frac{64}{3x-5}-4\right|&=\left|\frac{64-4(3x-5)}{3x-5}\right|\\ &=\left|\frac{84-12x}{3x-5}\right|\\ &=\left|\frac{12(7-x)}{3x-5}\right|\\ &=\left|\frac{12}{3x-5}\right||x-7|. \end{eqnarray}
$\endgroup$ 6
