Question

Rezolvati in Q+ ecuatiile
a)x-3/15=6/5
b)2/3x+5/6=17/18

Answer 1

$a)~x- \frac{3}{15}= \frac{6}{5 } \\ \\ x= \frac{6}{5}+ \frac{3}{15} \\ \\ x= \frac{6}{5}+ \frac{1}{5} \\ \\ \boxed{x= \frac{7}{5}} \\ \\ b)~ \frac{2}{3} x+ \frac{5}{6} = \frac{17}{18} \\ \\ \frac{2}{3}x= \frac{17}{18}- \frac{5}{6} \\ \\ \frac{2}{3}x= \frac{17}{18}- \frac{15}{18}$

$\frac{2}{3}x= \frac{2}{18} \Rightarrow x= \frac{2}{18} \cdot \frac{3}{2} \Leftrightarrow \boxed{x= \frac{1}{6} }.$

$In~cazul~in~care~x~era~la~numitor~(nu~mi-ai~confirmat~acest \\ lucru),~atunci~solutia~este~urmatoarea: \\ \\ \frac{2}{3x}+ \frac{5}{6}= \frac{17}{18} \\ \\ \frac{2}{3x}= \frac{17}{18}- \frac{5}{6} \\ \\ \frac{2}{3x}= \frac{2}{18} \Rightarrow x= \frac{2 \cdot 18}{2 \cdot 3} \Leftrightarrow \boxed{x=6}.$

Answer 2

x - 3/15 = 6/5
x - 1/5 = 6/5
x = 6/5 + 1/5
x = 7/5

2/3x + 5/6 = 17/18
2/3x = 17/18 - 5/6
2/3x = 17/18 - 15/18 amplific a doua fractie cu 3
2/3x = 2/18
x = 2/18 : 2/3
x = 2/18 · 3/2
x = 6/36 
x = 1/6