Răspuns:
14. a) [tex]\frac{7}{5}[/tex] + [tex]\frac{21x}{35}[/tex] = x x- [tex]\frac{21x}{35}[/tex] = [tex]\frac{7}{5}[/tex] aducem la acelasi numitor 35
35x-21x= 35 14 x= 35 x= 35/14= [tex]\frac{5*7}{2*7}[/tex]= [tex]\frac{5}{2}[/tex] x= [tex]\frac{5}{2}[/tex]
b) [tex]\frac{10}{3}[/tex] - [tex]\frac{5x}{15}[/tex] = x x+ [tex]\frac{5x}{15}[/tex] = [tex]\frac{10}{3}[/tex] 15x+5x= 5*10
20x= 50 => x= 50:20 =5/2 x= 5/2
c) [tex]\frac{9}{7}[/tex] - [tex]\frac{15x}{21}[/tex] = x x+ [tex]\frac{15x}{21}[/tex] = [tex]\frac{9}{7}[/tex] 21x+15x= 9*3
36x= 9*3=> x= 9*3: 4*9= 3/4 x= 3/4
d) [tex]\frac{18}{7}[/tex] + [tex]\frac{99x}{63}[/tex] = x x- [tex]\frac{99x}{63}[/tex] = [tex]\frac{18}{7}[/tex] 63x-99x= 18*9
-36x= 2*81 => x= - 2*81:36= - 9/2 x=-9/2
15.a) [tex]\frac{5}{2}[/tex] *[tex]\frac{6x}{9}[/tex] - [tex]\frac{5}{2} * \frac{4}{10}[/tex] = x [tex]\frac{15x}{9} -1= x[/tex] 15x-9x= 1*9
6x=9 => x= 9/6 x= 3/2
b) [tex]\frac{12}{10}[/tex] * [tex]\frac{3x}{9}[/tex] + [tex]\frac{12}{10} * \frac{75}{100}[/tex] =x x- [tex]\frac{4x}{10}[/tex] = [tex]\frac{9}{10}[/tex] 10x- 4x= 9
6x=9 x= 9/6 x= 3/2
c) [tex]\frac{4}{10} * \frac{15x}{9}[/tex] + [tex]\frac{4}{10} * \frac{5}{4}[/tex] = x x- [tex]\frac{2x}{3}[/tex] = [tex]\frac{1}{2}[/tex] 6x-4x= 3
2x=3 => x=3/2
d) [tex]\frac{25}{10} * \frac{12x}{90}[/tex] - [tex]\frac{25}{10} * \frac{16}{100}[/tex] = x x- [tex]\frac{x}{3}[/tex] = [tex]\frac{2}{5}[/tex] 15x-5x= 6
10x=6 x= 6/10 = 3/5 x= 3/5
16. a) [tex]\frac{5}{4} - \frac{1}{4} * \frac{1}{6x}[/tex] = [tex]\frac{6}{5}[/tex] [tex]\frac{5}{4}[/tex] - [tex]\frac{6}{5}[/tex] = [tex]\frac{1}{24x}[/tex] [tex]\frac{5*5-6*4}{20}[/tex]= [tex]\frac{1}{24x}[/tex] [tex]\frac{1}{20}[/tex]= [tex]\frac{1}{24x}[/tex]=>
24x= 20 => x= 20/24= 5/6 x=5/6
b) [tex]\frac{6}{5}[/tex] + [tex]\frac{2}{5}* \frac{1}{4x}[/tex] = [tex]\frac{4}{3}[/tex] [tex]\frac{4}{3} - \frac{6}{5}[/tex] = [tex]\frac{1}{10x}[/tex] [tex]\frac{20-18}{15}[/tex] = [tex]\frac{1}{10x}[/tex] [tex]\frac{2}{15}[/tex]= [tex]\frac{1}{10x}[/tex]=>
2*10x= 15*1 /:5 4x= 3 => x= 3/4
c) [tex]\frac{1}{3} * \frac{1}{5x}[/tex] - [tex]\frac{1}{3} * 7[/tex] = [tex]-\frac{5}{2}[/tex] [tex]\frac{1}{15x}[/tex] = [tex]\frac{7}{3} -\frac{5}{2}[/tex] [tex]\frac{1}{15x}[/tex] = [tex]\frac{14-15}{6}[/tex] = - [tex]\frac{1}{6}[/tex]
15x=-6 => x= -6/15 = -2/5 x= -2/5
