Question

What is x in the equation?
4/5 (x − 3/10) = −2 1/4

Answer 1

let's firstly convert the mixed fractions to improper fractions.

`\stackrel{mixed}{2(1)/(4)}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill`

`\cfrac{4}{5}\left( x-\cfrac{3}{10} \right)~~ = ~~-\cfrac{9}{4}\implies \cfrac{4x}{5}-\cfrac{6}{25}~~ = ~~-\cfrac{9}{4} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{100}}{100\left( \cfrac{4x}{5}-\cfrac{6}{25} \right)~~ = ~~100\left( -\cfrac{9}{4} \right)}\implies 80x-24=-225 \\\\\\ 80x=-201\implies x=-\cfrac{201}{80} \implies {\Large \begin{array}{llll} x=-2(41)/(80) \end{array}}`