Question

Resolva as seguintes equações.URGENTE

Answer 1

De acordo com os cálculos abaixo, as respostas são:

a)  $x\in\{\frac{89}{191}\}$

b)  $x\in\{17\}$

c)  $x\in\{\frac{33288}{1547}\}$

Vamos entender o porquê?

a)

    $\dfrac{5x-3}{2}-\dfrac{1-x}{\dfrac{3}{2}}=\dfrac{1}{2}\times\dfrac{1-4x}{\dfrac{5}{8}}\Leftrightarrow$

$\Leftrightarrow\dfrac{5x-3}{2}-\dfrac{2(1-x)}{3}=\dfrac{1}{2\!\!\!/}\times\dfrac{8\!\!\!/(1-4x)}{5}\Leftrightarrow$

$\Leftrightarrow\dfrac{5x-3}{2}-\dfrac{2-2x}{3}=\dfrac{4(1-4x)}{5}\Leftrightarrow$

$\Leftrightarrow\dfrac{5x-3}{2}-\dfrac{2-2x}{3}=\dfrac{4-16x}{5}\Leftrightarrow$

$\Leftrightarrow\dfrac{5x-3}{2}-\dfrac{2-2x}{3}-\dfrac{4-16x}{5}=0\Leftrightarrow$

$\Leftrightarrow\dfrac{15(5x-3)}{2\times15}-\dfrac{10(2-2x)}{3\times10}-\dfrac{6(4-16x)}{5\times6}=0\Leftrightarrow$

$\Leftrightarrow\dfrac{75x-45}{30}-\dfrac{20-20x}{30}-\dfrac{24-96x}{30}=0\Leftrightarrow$

$\Leftrightarrow\dfrac{(75x-45)-(20-20x)-(24-96x)}{30}=0\Leftrightarrow$

$\Leftrightarrow\dfrac{75x-45-20+20x-24+96x}{30}=0\Leftrightarrow$

$\Leftrightarrow75x-45-20+20x-24+96x=0\Leftrightarrow$

$\Leftrightarrow75x+20x+96x=45+20+24\Leftrightarrow$

$\Leftrightarrow191x=89\Leftrightarrow$

$\Leftrightarrow x=\dfrac{89}{191}$

b)

    $\dfrac{x-1}{4}-\dfrac{1}{8}\left(\dfrac{x-5}{4}-\dfrac{14-2x}{5}\right)=\dfrac{x-9}{2}-\dfrac{7}{8}\Leftrightarrow$

$\Leftrightarrow\dfrac{x-1}{4}-\dfrac{1}{8}\left(\dfrac{5(x-5)}{4\times5}-\dfrac{4(14-2x)}{5\times4}\right)=\dfrac{4(x-9)}{2\times4}-\dfrac{7}{8}\Leftrightarrow$

$\Leftrightarrow\dfrac{x-1}{4}-\dfrac{1}{8}\left(\dfrac{5x-25}{20}-\dfrac{56-8x}{20}\right)=\dfrac{4x-36}{8}-\dfrac{7}{8}\Leftrightarrow$

$\Leftrightarrow\dfrac{x-1}{4}-\dfrac{1}{8}\left(\dfrac{(5x-25)-(56-8x)}{20}\right)=\dfrac{4x-36-7}{8}\Leftrightarrow$

$\Leftrightarrow\dfrac{x-1}{4}-\dfrac{1}{8}\left(\dfrac{5x-25-56+8x}{20}\right)=\dfrac{4x-43}{8}\Leftrightarrow$

$\Leftrightarrow\dfrac{x-1}{4}-\dfrac{1}{8}\left(\dfrac{13x-81}{20}\right)=\dfrac{4x-43}{8}\Leftrightarrow$

$\Leftrightarrow\dfrac{x-1}{4}-\dfrac{13x-81}{20\times8}=\dfrac{4x-43}{8}\Leftrightarrow$

$\Leftrightarrow\dfrac{x-1}{4}-\dfrac{13x-81}{160}-\dfrac{4x-43}{8}=0\Leftrightarrow$

$\Leftrightarrow\dfrac{40(x-1)}{4\times40}-\dfrac{13x-81}{160}-\dfrac{20(4x-43)}{8\times20}=0\Leftrightarrow$

$\Leftrightarrow\dfrac{40x-40}{160}-\dfrac{13x-81}{160}-\dfrac{80x-860}{160}=0\Leftrightarrow$

$\Leftrightarrow\dfrac{(40x-40)-(13x-81)-(80x-860)}{160}=0\Leftrightarrow$

$\Leftrightarrow40x-40-13x+81-80x+860=0\Leftrightarrow$

$\Leftrightarrow40x-13x-80x=40-81-860\Leftrightarrow$

$\Leftrightarrow-53x=-901\Leftrightarrow$

$\Leftrightarrow x=\dfrac{-901}{-53}\Leftrightarrow$

$\Leftrightarrow x=17$

c)

    $\dfrac{\dfrac{3x}{4}-2}{8}+19=x-\dfrac{\dfrac{x}{2}+1-\dfrac{1}{5}(x-4)}{11}\Leftrightarrow$

$\Leftrightarrow\dfrac{\dfrac{3x}{4}-\dfrac{2\times4}{4}}{8}+19=x-\dfrac{\dfrac{x}{2}+1-\dfrac{x-4}{5}}{11}\Leftrightarrow$

$\Leftrightarrow\dfrac{\dfrac{3x}{4}-\dfrac{8}{4}}{8}+19=x-\dfrac{\dfrac{5x}{2\times5}+\dfrac{1\times10}{10}-\dfrac{2(x-4)}{5\times2}}{11}\Leftrightarrow$

$\Leftrightarrow\dfrac{\dfrac{3x-8}{4}}{8}+19=x-\dfrac{\dfrac{5x}{10}+\dfrac{10}{10}-\dfrac{2x-8}{10}}{11}\Leftrightarrow$

$\Leftrightarrow\dfrac{3x-8}{4\times8}+19=x-\dfrac{\dfrac{5x+10-(2x-8)}{10}}{11}\Leftrightarrow$

$\Leftrightarrow\dfrac{3x-8}{32}+19=x-\dfrac{5x+10-2x+8}{10\times11}\Leftrightarrow$

$\Leftrightarrow\dfrac{3x-8}{32}+\dfrac{19\times32}{32}=\dfrac{110x}{110}-\dfrac{3x+18}{110}\Leftrightarrow$

$\Leftrightarrow\dfrac{3x-8}{32}+\dfrac{608}{32}=\dfrac{110x-(3x+18)}{110}\Leftrightarrow$

$\Leftrightarrow\dfrac{3x-8+608}{32}=\dfrac{110x-3x-18}{110}\Leftrightarrow$

$\Leftrightarrow\dfrac{3x+600}{32}=\dfrac{107x-18}{110}\Leftrightarrow$

$\Leftrightarrow\dfrac{55(3x+600)}{32\times55}=\dfrac{16(107x-18)}{110\times16}\Leftrightarrow$

$\Leftrightarrow\dfrac{165x+33000}{1760}=\dfrac{1712x-288}{1760}\Leftrightarrow$

$\Leftrightarrow165x+33000=1712x-288\Leftrightarrow$

$\Leftrightarrow165x-1712x=-288-33000\Leftrightarrow$

$\Leftrightarrow-1547x=-33288\Leftrightarrow$

$\Leftrightarrow x=\dfrac{-33288}{-1547}\Leftrightarrow$

$\Leftrightarrow x=\dfrac{33288}{1547}$

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