Question

1/3 (2x + 1) +x = 1/2????

Answer 1

$\frac{1}{3}\left(2x+1\right)+x=\frac{1}{2}$

$\mathrm{Multiplicar\:ambos\:os\:lados\:por\:}3\\ \frac{1}{3}\left(2x+1\right)\cdot \:3+x\cdot \:3=\frac{1}{2}\cdot \:3$

$\mathrm{Simplificar}\\ 2x+1+3x=\frac{3}{2}\\ 5x+1=\frac{3}{2}$

$\mathrm{Subtrair\:}1\mathrm{\:de\:ambos\:os\:lados}\\ 5x+1-1=\frac{3}{2}-1$

$\mathrm{Simplificar}\\ 5x+1-1=\frac{3}{2}-1\\ \mathrm{Simplificar\:}5x+1-1:\quad 5x\\ 5x+1-1\\ \mathrm{Somar\:elementos\:similares:}\:1-1=0\\ =5x\\ \mathrm{Simplificar\:}\frac{3}{2}-1:\quad \frac{1}{2}\\ \frac{3}{2}-1\\ \mathrm{Converter\:para\:fracao}:\quad \:1=\frac{1\cdot \:2}{2}\\ =-\frac{1\cdot \:2}{2}+\frac{3}{2}\\ \mathrm{Ja\:que\:os\:denominadores\:sao\:iguais,\:combinar\:as\:fracoes}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\ =\frac{-1\cdot \:2+3}{2}\\ =\frac{1}{2}$

$\mathrm{Simplificar}\\ \frac{5x}{5}=\frac{\frac{1}{2}}{5}\\ \mathrm{Simplificar\:}\frac{5x}{5}:\quad x\\ \frac{5x}{5}\\ \frac{5x}{5}\\ \mathrm{Dividir:}\:\frac{5}{5}=1\\ =x\\ \mathrm{Simplificar\:}\frac{\frac{1}{2}}{5}:\quad \frac{1}{10}\\ \frac{\frac{1}{2}}{5}\\ \mathrm{Aplicar\:as\:propriedades\:das\:fracoes}:\quad \frac{\frac{b}{c}}{a}=\frac{b}{c\:\cdot \:a}\\ =\frac{1}{2\cdot \:5}\\ \mathrm{Multiplicar\:os\:numeros:}\:2\cdot \:5=10\\ =\frac{1}{10}\\ x=\frac{1}{10}$

A resposta é $x=\frac{1}{10}$