Matemática, perguntado por victorialinda1, 1 ano atrás

Determine o conjunto solução, no domínio R, das equações a seguir.

b) x+/2 - 2.(2-x)/3 = x - 5x + 14/6.

c) 2.(x-2)+3x/4 - x-3.(2x+9)/5 + x+4/10= 7x/20+2x​

Soluções para a tarefa

Respondido por GeBEfte
5

Tenha atenção na utilização da propriedade distributiva da multiplicação e com os sinais.

b)

\frac{x}{2}-2\,.\,\frac{2-x}{3}~=~x-5x+\frac{14}{6}\\\\\\Vamos~comecar~achando~o~MMC~entre~os~denominadores~2,3\,e\,6\\MMC(2,3,6)~=~2~.~3~=~\boxed{6}\\\\\\\frac{3\,.\,x~-~2\,.\,2\,.\,(2-x)}{6}~=~\frac{6\,.\,x~-~6\,.\,5x~+~1\,.\,14}{6}

\frac{3x~-~4\,.\,(2-x)}{6}~=~\frac{6x~-~30x~+~14}{6}\\\\\\Podemos~simplificar~os~denominadores\\\\\\3x-4\,.\,(2-x)~=~6x-30x+14\\\\\\3x-8+4x~=~-24x+14\\\\\\3x+4x+24x~=~14+8\\\\\\31x~=~22\\\\\\\boxed{x~=~\frac{22}{31}}

c)

2\,.\,(x-2)+\frac{3x}{4}-x-3\,.\,\frac{2x+9}{5}+x+\frac{4}{10}~=~\frac{7x}{20}+2x\\\\\\MMC~=~2~.~2~.~5~=~\boxed{20}\\\\\\\frac{20\,.\,2\,.\,(x-2)~+~5\,.\,3x~-~20\,.\,x~-~4\,.\,3\,.\,(2x+9)~+\,20\,.\,x~+~2\,.\,4}{20}~=~\frac{1\,.\,7x~+~20\,.\,2x}{20}

Podemos~simplificar~os~denominadores\\\\\\20\,.\,2\,.\,(x-2)~+~5\,.\,3x~-~20\,.\,x~-~4\,.\,3\,.\,(2x+9)~+\,20\,.\,x~+~2\,.\,4~=~1\,.\,7x~+~20\,.\,2x

40\,.\,(x-2)~+~15x~-~20x~-~12\,.\,(2x+9)~+\,20x~+~8~=~7x~+~40x\\\\\\40x-80+15x-20x-24x-108+20x+8~=~47x\\\\\\40x+15x-20x-24x+20x-47x~=~80+108-8\\\\\\-16x~=~180\\\\\\x~=~\frac{180}{-16}\\\\\\\boxed{x~=~-\frac{45}{4}~~ou~~x~=~-11,25}


victorialinda1: muito obg
victorialinda1: parabéns
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