Question

Resolva as equações fracionais de 1° grau:

a) x/2 + x/3 = 5

b) x/2 + x/3 + x/4 = 13

c) x+3/4 + x+1/6 = 3

d) x-2/3 + x-3/2 = x+5/5

e) x+9/3 + x+5/4 + x+7/5 = 8

f) x-1/4 - x-3/5 = 1-2x/20

g) 4x+1/2 - 2-3x/4 = 26-x/6

Answer 1

Resposta:

Explicação passo-a-passo:

a)

$\:\frac{x}{2}+\:\frac{x}{3}\:=\:5\\\\\frac{x}{2}\cdot \:6+\frac{x}{3}\cdot \:6=5\cdot \:6\\\\5x=30\\\\x=\frac{30}{5} \\\\x=6$

b)

$\frac{x}{2}\:+\:\frac{x}{3}\:+\:\frac{x}{4}\:=\:13\\\\\frac{x}{2}\cdot \:12+\frac{x}{3}\cdot \:12+\frac{x}{4}\cdot \:12=13\cdot \:12\\\\6x+4x+3x=156\\\\13x=156\\\\x=\frac{156}{13}\\\\x=12$

c)

$x+\frac{3}{4}\:+\:x+\frac{1}{6}\:=\:3\\\\x+x+\frac{3}{4}+\frac{1}{6}=3\\\\2x+\frac{3}{4}+\frac{1}{6}=3\\\\2x+\frac{9}{12}+\frac{2}{12}=3\\\\2x+\frac{11}{12}=3\\\\2x=3-\frac{11}{12}\\\\2x=\frac{25}{12}\\\\x=\frac{25}{24}$

d)

$x-\frac{2}{3}\:+\:x-\frac{3}{2}\:=\:x+\frac{5}{5}\\\\-\frac{2}{3}+x-\frac{3}{2}=\frac{5}{5}\\\\x-\frac{2}{3}-\frac{3}{2}=\frac{5}{5}\\\\x-\frac{4}{6}-\frac{9}{6}=\frac{5}{5}\\\\x-\frac{13}{6}=\frac{5}{5}\\\\x=1+\frac{13}{6}\\\\x=\frac{19}{6}$

e)

$x+\frac{9}{3}\:+\:x+\frac{5}{4}\:+\:x+\frac{7}{5}\:=\:8\\\\x+x+x+\frac{9}{3}+\frac{5}{4}+\frac{7}{5}=8\\\\3x+\frac{9}{3}+\frac{5}{4}+\frac{7}{5}=8\\\\3x+3+\frac{5}{4}+\frac{7}{5}=8\\\\3x+\frac{3}{1}+\frac{5}{4}+\frac{7}{5}=8\\\\3x+\frac{113}{20}=8\\\\3x=8-\frac{113}{20}\\\\3x=\frac{47}{20}\\\\x=\frac{47}{60}$

f)

$x-\frac{1}{4}\:-\:x-\frac{3}{5}\:=\:1-\frac{2x}{20}\\\\x-x-\frac{1}{4}-\frac{3}{5}=1-\frac{2x}{20}\\\\-\frac{1}{4}-\frac{3}{5}=1-\frac{2x}{20}\\\\-\frac{5}{20}-\frac{12}{20}=1-\frac{2x}{20}\\\\\frac{-5-12}{20}=1-\frac{2x}{20}\\\\\frac{-17}{20}=1-\frac{2x}{20}\\\\0=\frac{37}{20}-\frac{x}{10}\\\\\frac{x}{10}=\frac{37}{20}\\\\x=\frac{37}{2}$

g)

$4x+\frac{1}{2}\:-\:2-\frac{3x}{4}\:=\:26-\frac{x}{6}\\\\4x-\frac{3}{2}-\frac{3x}{4}=26-\frac{x}{6}\\\\4x\cdot \:12-\frac{3}{2}\cdot \:12-\frac{3x}{4}\cdot \:12=26\cdot \:12-\frac{x}{6}\cdot \:12\\\\39x-18=312-2x\\\\39x=-2x+330\\\\41x=330\\\\x=\frac{330}{41}$