Question

ME AJUDEM POR FAVOR! É PARA AMANHÃ.
Determine a solução das equações a seguir, considerando U = Q.
a) X/2 + 3x/2 = 1 - 7/10
b) 2x + 2/3 = 3x + 2
c) 2x/5 + 3x - 2 = X + 10
d) 1x/2 - 3x - 1/3 = 8x + 12

Answer 1

Olá!

Questão a)

$\dfrac{x}{2}+\dfrac{3x}{2} ~=~\dfrac{1}{1} -\dfrac{7}{10} ~~~~~~~~~~\to ~~~~~~~~~~\dfrac{x+3x}{2}~=~\dfrac{10-7}{10} \\ \\ \\ \\ \dfrac{4x}{2}~=~\dfrac{3}{10} ~~~~~\to ~~~~~2x~=~\dfrac{3}{10}~~~~~~~\to~~~~~~~x=\dfrac{\frac{3}{10} }{2} \\ \\ \\ \\ x=\dfrac{3}{10}\times\dfrac{1}{2} ~~~~~~~~~~\to~~~~~~~~~~\boxed{x=\dfrac{3}{20} }$

Questão b)

$2x+\dfrac{2}{3} ~=~3x+2 ~~~~~~~~~~\to ~~~~~~~~~~2x-3x~=~2-\dfrac{2}{3} \\ \\ \\ \\-x~=~\dfrac{6-2}{3} ~~~~~\to ~~~~~-x~=~\dfrac{4}{3}~~~~~~~\to~~~~~~~\boxed{x=-\dfrac{4}{3} }$

Questão c)

$\dfrac{2x}{5}+3x-2 ~=~x+10 ~~~~~~~~~~\to ~~~~~~~~~~\dfrac{2x}{5} +3x-x~=~10+2\\ \\ \\ \\ \dfrac{2x}{5} +\dfrac{2x}{1} ~=~12~~~~~~~\to~~~~~~\dfrac{2x+10x}{5}~=~12~~~~~\to~~~~~12x=60 \\ \\\\ \\ x=\dfrac{60}{12} ~~~~~~\to~~~~~~ \boxed{x=5 }$

Questão d)

$\dfrac{x}{2}-3x-\dfrac{1}{3} ~=~8x+12 ~~~~~~~~~~\to ~~~~~~~~~~\dfrac{x}{2}-3x-8x} ~=~12+\dfrac{1}{3} \\ \\ \\ \\ \dfrac{x}{2}-11x} ~=~\dfrac{36+1}{3} ~~~~~\to ~~~~~\dfrac{x-22x}{2} =\dfrac{37}{3} ~~~~~~\to~~~~~~\dfrac{-21x}{2} =\dfrac{37}{3} \\ \\ \\ \\ -63x=74~~~~~~\to~~~~~~\boxed{x=-\dfrac{74}{63} }$

:)