Question

Resolva as seguintes equações:
a) $\frac{x+3}{4} +\frac{x+1}{6} =3$
b)$\frac{x+8}{5}+ \frac{x+2}{2}=4$

Answer 1

Resposta:

a) x=5

b) x=2

Explicação passo-a-passo:

a)

$\displaystyle \frac{x+3}{4} +\frac{x+1}{6} =3$

mmc(4,6)

4,6|2

2,3|2

1,3|3

1,1

mmc(4,6)=2.2.3=12

$\displaystyle \frac{x+3}{4} +\frac{x+1}{6} =3\\\\\frac{3(x+3)+2(x+1)}{\diagup\!\!\!\!\!12} =\frac{36}{\diagup\!\!\!\!\!12} \\\\3x+9+2x+2=36\\5x+11=36\\5x=36-11=25\\x=\frac{25}{5} =5$

b)

$\displaystyle \frac{x+8}{5} +\frac{x+2}{2} =4$

mmc(5,2)

5,2|2

5,1|5

1,1

mmc(5,2)=10

$\displaystyle \frac{x+8}{5} +\frac{x+2}{2} =4\\\\\frac{2(x+8)+5(x+2)}{\diagup\!\!\!\!\!10} =\frac{40}{\diagup\!\!\!\!\!10} \\\\2x+16+5x+10=40\\7x+26=40\\7x=40-26=14\\x=\frac{14}{7} =2$