Question

Să se rezolve ecuațiile următoare:
$a).\frac{5}{3} x \: + \frac{2}{9} = 1 \ \frac{1}{3}$
$b). \frac{2}{3} x \: - 1 = 1.(3)$
$c). \frac{5}{6} x - 1 \frac{1}{2} = 0.25$

Answer 1

a
[tex] \frac{5}{3} x + \frac{2}{9} = 1 \frac{1}{3} \\ \frac{5}{3} x + \frac{2}{9} = \frac{4}{3} \\ \frac{15}{9} x + \frac{2}{9} = \frac{12}{9} \\ \frac{15}{9} x= \frac{12}{9} - \frac{2}{9} \\ \frac{15}{9} x= \frac{10}{9} \\ 15x=10 \\ x = \frac{10}{15} \\ x= \frac{2}{3} [/tex]

b
$\frac{2}{3} x-1=1,(3) \\ \frac{2}{3} x= \frac{12}{9} +1 \\ \frac{2}{3} x= \frac{12}{9} + \frac{9}{9} \\ \frac{2}{3} x= \frac{21}{9} \\ \frac{2}{3}x= \frac{7}{3} \\ 2x=7 \\ x= \frac{7}{2}$

c
$\frac{5}{6} x-1 \frac{1}{2} = 0,25 \\ \frac{5}{6}x- \frac{3}{2} = \frac{25}{100} \\ \frac{5}{6}x- \frac{3}{2} = \frac{1}{4} \\ \frac{5}{6} x = \frac{1}{4} + \frac{3}{2} \\ \frac{5}{6} x = \frac{1}{4} + \frac{6}{4} \\ \frac{5}{6} x = \frac{7}{4} \\ x= \frac{7}{4} : \frac{5}{6} \\ x= \frac{7}{4} x \frac{6}{5} \\ x= \frac{21}{10}$