Question

inequação, pfv ajudem
a) x/3 - 1/2 < 5/6

b) 3/4 - x/2 < 5/4

Answer 1

a) 

$\mathsf{\dfrac{x}{3}-\dfrac{1}{2}\ \textless \ \dfrac{5}{6}}\\\\\\\mathsf{\dfrac{2\cdot x}{2\cdot 3}-\dfrac{3\cdot 1}{3\cdot 2}\ \textless \ \dfrac{5}{6}}\\\\\\\mathsf{\dfrac{2x}{\diagup\!\!\!\!6}-\dfrac{3}{\diagup\!\!\!\!6}\ \textless \ \dfrac{5}{\diagup\!\!\!\!6}}\\\\\\\mathsf{2x-3\ \textless \ 5}\\\\\\\mathsf{2x\ \textless \ 5+3}\\\\\\\mathsf{2x\ \textless \ 8}\\\\\\\mathsf{x\ \textless \ \dfrac{8}{2}}\\\\\\\boxed{\mathsf{x\ \textless \ 4}}\: \: \checkmark$

= = = = = 

b) 

$\mathsf{\dfrac{3}{4}-\dfrac{x}{2}\ \textless \ \dfrac{5}{4}}\\\\\\\mathsf{\dfrac{3}{4}-\dfrac{2\cdot x}{2\cdot 2}\ \textless \ \dfrac{5}{4}}\\\\\\\mathsf{\dfrac{3}{\diagup\!\!\!\!4}-\dfrac{2x}{\diagup\!\!\!\!4}\ \textless \ \dfrac{5}{\diagup\!\!\!\!4}}\\\\\\\mathsf{3-2x\ \textless \ 5}\\\\\\\mathsf{-2x\ \textless \ 5-3}\\\\\\\mathsf{-2x\ \textless \ 2}\\\\\\\mathsf{-x\ \textless \ \dfrac{2}{2}}\\\\\\\mathsf{-x\ \textless \ 1}\\\\\\\boxed{\mathsf{x\ \textgreater \ -1}}\: \: \checkmark$