Question

$1\frac{2}{3}$ ÷ 5,5 + $1\frac{7}{12}$ ÷ ( 2,25 - X ) = $\frac{7}{6}$ Fazer explicando por favor

Answer 1

Resposta:

x= $\frac{95}{228}$

Explicação passo-a-passo:

$1\frac{2}{3}$ = $\frac{3.1+2}{3}$=$\frac{5}{3}$

5,5 = $\frac{55}{10} = \frac{11}{2}$

$1\frac{7}{12} = \frac{12.1+7}{12} = \frac{19}{12}$

2,25 = $\frac{225}{100} = \frac{9}{4}$

logo temos:

$\frac{5}{3}$÷$\frac{11}{2}$+$\frac{19}{12}$÷$(\frac{9}{4} -x)$ = $\frac{7}{6}$ = $\frac{5}{3}$÷$\frac{11}{2}$+$\frac{19}{12}$÷$(\frac{9-4x}{4})$ = $\frac{7}{6}$ na divisão de fração, repetimos a primeira e multiplicamos pelo inverso da segunda

$\frac{5}{3} . \frac{2}{11} + \frac{19}{12} . \frac{4}{9-4x} = \frac{7}{6}$ =>  $\frac{10}{33} + \frac{76}{108-48x} = \frac{7}{6}$ =>  $\frac{76}{108-48x} = \frac{7}{6} - \frac{10}{33} => \frac{76}{108-48x} = \frac{77-20}{66}$  => $\frac{76}{108-48x} = \frac{57}{66}$ multiplicando cruzado temos:

5016 = 6156 - 2736x => 5016-6156 = -2736x => -2736x = -1140

x= $\frac{-1140}{-2736} => x= \frac{1140}{2736}$

x= $\frac{95}{228}$