Question

Aflati X stiind ca: A) x+5(intreg) 5 pe 6 -2(intreg) 1 pe 2=6(intregi) 3 pe 4 B)8(intregi)-x= 4(intregi) 1 pe 7 va roog mult ajutatima

Answer 1

 

$\displaystyle\\A)\\\\x+5\frac{5}{6}-2\frac{1}{2}=6\frac{3}{4}\\\\\text{Introducem intregii in fractie.}\\\\x+\frac{5\cdot6+5}{6}-\frac{2\cdot2+1}{2}=\frac{6\cdot4+3}{4}\\\\x+\frac{35}{6}-\frac{5}{2}=\frac{27}{4}\\\\x=\frac{27}{4}-\frac{35}{6}+\frac{5}{2}\\\\\text{Aducem la acelasi numitor.}\\\\x=\frac{27\cdot3}{4\cdot3}-\frac{35\cdot2}{6\cdot2}+\frac{5\cdot6}{2\cdot6}\\\\x=\frac{81}{12}-\frac{70}{12}+\frac{30}{12}\\\\x=\frac{81-70+30}{12}\\\\x=\frac{41}{12}\\\\\boxed{x=3\frac{5}{12}}$

$\displaystyle\\B)\\\\8-x=4\frac{1}{7}\\\\x=8-4\frac{1}{7}\\\\x=8-\frac{4\cdot7+1}{7}\\\\x=8-\frac{29}{7}\\\\x=\frac{8\cdot7}{7}-\frac{29}{7}\\\\x=\frac{56}{7}-\frac{29}{7}\\\\x=\frac{56-29}{7}\\\\x=\frac{27}{7}\\\\\boxed{x=3\frac{6}{7}}$