Question

Exercițiul 5: f), g) ,h) ,i) ,j)

Answer 1

$5f)\displaystyle \frac{4}{5} x+ \frac{3}{4} = \frac{1}{2} x+3 \frac{1}{2} \\ \\ \frac{4}{5} x+ \frac{3}{4} = \frac{1}{2} x+ \frac{7}{2} \\ \\ 16x+15=10x+70 \\ \\ 16x-10x=70-15 \\ \\ 6x=55 \Rightarrow \boxed{x= \frac{55}{6} }$

$\displaystyle g)3,14x+0,(63)=2,14x+1,1(6) \\ \\ \frac{314}{100} x+ \frac{63}{99} = \frac{214}{100} x+ \frac{116-11}{90} \\ \\ \frac{314}{100} x+ \frac{63}{99} = \frac{214}{100} x+ \frac{105}{90} \\ \\ \frac{157}{50} x+ \frac{7}{11} = \frac{107}{50} x+ \frac{7}{6} \\ \\ 5181x+1050=3531x+1925 \\ \\ 5181x-3531x=1925-1050 \\ \\ 1650x=875 \Rightarrow x= \frac{875}{1650} \Rightarrow \boxed{x= \frac{35}{66} }$

$\displaystyle h)x \cdot 2,4=0,576 \\ \\ x \cdot \frac{24}{10} = \frac{576}{1000} \\ \\ 2400x=576 \Rightarrow x= \frac{576}{2400} \Rightarrow \boxed{x= \frac{6}{25} }$

$\displaystyle i)2,415:x=1,05 \\ \\ \frac{2415}{1000} :x= \frac{105}{100} \\ \\ \frac{2415}{1000} \cdot \frac{1}{x} = \frac{105}{100} \\ \\ \frac{2415}{1000x} = \frac{105}{100} \\ \\ 105000x=241500 \Rightarrow x= \frac{241500}{105000} \Rightarrow \boxed{x= \frac{23}{10} }$

$\displaystyle j)6,24-2x=3,12 \\ \\ \frac{624}{100} -2x= \frac{312}{100} \\ \\ 624-200x=312 \\ \\ -200x=312-624 \\ \\ -200x=-312 \Rightarrow x= \frac{312}{200} \Rightarrow \boxed{ x=\frac{39}{25} }$