Question

02. Resolva as seguintes equações na variável x, sendo U-R:
$a \: \frac{x}{2} - \frac{ x}{3} = 5$
$b \: \frac{x}{5} + \frac{x}{4} = 3$
$c \: \frac{x}{6} + \frac{x}{4} = 5$
$d \: \frac{x + 1}{3} + \frac{x + 2}{4} = 2$
$e \: \frac{x + 1}{3} - \frac{x + 3}{5} = 2$
​

Answer 1

Explicação passo-a-passo:

.

$\dfrac{x}{2} - \dfrac{x}{ 3} = 5$

$3x - 2x = 30$

$x = 30$

.

$\dfrac{x}{5} + \dfrac{x}{4} = 3$

$4x + 5x = 60$

$9x = 60$

$x = \dfrac{60 \div 3}{9 \div 3}$

$x = \dfrac{20}{3}$

.

$\dfrac{x}{6} + \dfrac{x}{4} = 5$

$2x + 3x = 60$

$5x = 60$

$x = \dfrac{60}{5}$

$x = 12$

.

$\dfrac{x + 1}{3} + \dfrac{x + 2}{4} = 2$

$4(x + 1) + 3(x + 2) = 24$

$4x + 4 + 3x + 6 = 24$

$7x + 10 = 24$

$7x = 24 - 10$

$7x = 14$

$x = \dfrac{14}{7}$

$x = 2$

.

$\dfrac{x + 1}{3} - \dfrac{x + 3}{5} = 2$

$5(x + 1) - 3(x + 3) = 30$

$5x + 5 - 3x - 9 = 30$

$2x - 4 = 30$

$2x = 30 + 4$

$2x = 34$

$x = \dfrac{34}{2}$

$x = 17$