Question

8. Determine a raiz das seguintes equações do 1° grau com uma incógnita:

d)
$\frac{x}{5} = 21 - \frac{x}{2}$

e)
$\frac{4}{5} + \frac{3x}{4} = \frac{1}{10} + x$

f)
$\frac{1}{6} - \frac{x}{2} = \frac{2x}{3} + \frac{1}{4}$
​

Answer 1

d) $\frac{x}{5}=21-\frac{x}{2}$

$\frac{2x}{10}=\frac{210}{10}-\frac{5x}{10}$

$\frac{2x}{10}=\frac{210-5x}{10}$

$2x=210-5x$

$2x+5x=210$

$7x=210$

$x=\frac{210}{7}$

$x=30$

e) $\frac{4}{5}+\frac{3x}{4}=\frac{1}{10}+x$

$\frac{16}{20}+\frac{15x}{20}=\frac{2}{20}+\frac{20x}{20}$

$\frac{16+15x}{20}=\frac{2+20x}{20}$

$16+15x=2+20x$

$15x-20x=2-16$

$-5x=-14$

$5x=14$

$x=\frac{14}{5}$

f) $\frac{1}{6}-\frac{x}{2}=\frac{2x}{3}+\frac{1}{4}$

$\frac{2}{12}-\frac{6x}{12}=\frac{8x}{12}+\frac{3}{12}$

$\frac{2-6x}{12}=\frac{8x+3}{12}$

$2-6x=8x+3$

$-6x-8x=3-2$

$-14x=1$

$x=-\frac{1}{14}$