Question

Como resolvo equações de 1 grau ? explique

Answer 1

Olá Lavinia,

vou dar 4 exemplos de equações do 1° grau..

$\boxed{1}~~2(x+3)=x-1\\\\ \boxed{2}~~ \dfrac{x}{x+1}= \dfrac{3}{2}\\\\\\ \boxed{3}~~x+\dfrac{x-1}{2}=7\\\\\boxed{4}~~2+\dfrac{x-2}{3}+\dfrac{1}{4}x=x+9$

Resoluções..

1.

$2(x+3)=x-1~~(aplica~a~distributiva)\\ 2x+6=x-1~~(troca~o~sinal~quando~troca~de~membro)\\ 2x-x=-1-6\\ x=-7\\\\ U=\mathbb{Z}\Rightarrow~~\boxed{S=\{-7\}}$

2.

$\dfrac{x}{x+1}= \dfrac{3}{2}~~(multiplica~cruzado)\\\\ 2\cdot x=3\cdot(x+1)\\ 2x=3x+3\\ 2x-3x=3\\ -x=3~~(multiplica~por~-1)\\ x=-3\\\\ U=\mathbb{Z}\Rightarrow~~\boxed{S=\{-3\}}\\\\\begin{cases}condicao~para~o~denominador~de~uma~fracao~algebrica:\\x+1\neq0\Rightarrow~x\neq-1\end{cases}$


3.

$x+ \dfrac{x-1}{2}=7~~(multiplica~os~termos~inteiros~pelo~denominador~2)\\\\ 2\cdot x+(x-1)=2\cdot7\\ 2x+x-1=14\\ 3x=14+1\\ 3x=15\\\\ x= \dfrac{15}{3}\\\\ x=5\\\\ U=\mathbb{N}\Rightarrow~~\boxed{S=\{5\}}$


4.

$2+ \dfrac{x-2}{3}+ \dfrac{1}{4}x=x+9~~(cria~um~denominador~para~2~e~x+9)\\\\ \dfrac{4}{2}+ \dfrac{x-2}{3}+ \dfrac{1}{4}x= \dfrac{3x+27}{3}~~(tira~MMC~de~2,3~e~4)=12\\\\ \dfrac{6\cdot4+4\cdot(x-2)+3\cdot x}{12}= \dfrac{4\cdot(3x+27)}{12}(nesta~parte~divida~o~denomi-\\\\ comum~pelos~antigos~denominadores,~e~multiplique~pelos~numera-\\ dores~correspondentes~e~cancele~o~denominador)..\\\\ 24+8x-8+3x=12x+108\\ 8x+3x-12x=108-24+8\\ -x=92~~(multiplica~por~-1)\\\\ x=-92\\\\ \boxed{S=\{-92\}}$

Espero ter ajudado e tenha ótimos estudos ;D