Calculate the value of $x$

Question

Given $\frac {11}2x - \frac {13} 3 = \frac 85$

So far, I have reached $33x = \frac{48}5 - 26$.

However I cannot figure out how to progress further.

Answer 1

From the point you reached, multiply throught by $5$. This is equivalent to multiplying by $\mathrm{lcm}(2,3,5) = 30$ from the start. It is easier to get rid of fractions and work in integers till the very last step.

You get $165x = 48+130 = 178$

$\therefore x = \frac{178}{165} = 1\frac{13}{165}$.

Note that your working has a sign error. You need to fix that.