Question

Equação: x+7/10=1/2
2) x+4/15=2/3
3)x+4/3=x+3/4
4)4x-7/3=5x/3
5)5x-1/18=11-x/18
6) a)x/6+1/12=1/4
b)x/6-1/3=1/2
c)x+x/3=8
d)x/3-1=x/4

Answer 1

1 ) $\frac{x+7}{10} = \frac{1}{2} => 2(x+7) = 10 => 2x+14 = 10 => 2x = 10-14 => 2x = -4 => x = -\frac{4}{2} => x = -2$

2 ) $\frac{x+4}{15} = \frac{2}{3} => 3(x+4) = 30 => 3x+12 = 30 => 3x = 30-12 => 3x = 18 => x = \frac{18}{3} => x = 6$

3 ) $\frac{x+4}{3} = \frac{x+3}{4} => 4(x+4) = 3(x+3) => 4x+16 = 3x+9 => 4x-3x = 9-16 => x = -7$

4 ) $\frac{4x-7}{3} = \frac{5x}{3} => 3(5x) = 3(4x-7) => 15x = 12x-21 => 15x-12x = -21 => 3x = -21 => x = -\frac{21}{3} => -7$

5 ) $\frac{5x-1}{18} = \frac{11-x}{18} => 18(5x-1) = 18(11-x) => 90x-18 = 198x-18 => 90x-198x = -18+18 => -108x = 0$

Essa 5º está alguma coisa errada, não pode se dividir 0, logo é indeterminada..

6 )
a )$\frac{ \frac{x}{6}+1}{12} = \frac{1}{4} => 4( \frac{x}{6} + 1) = 12 => \frac{12x}{6}+4 = 12 => \frac{12x+24}{6} = 12 => 12x+24 = 72 => 12x = 72-24 => x = \frac{48}{12} => x = 4$

b ) $\frac{ \frac{x}{6} -1}{3} = \frac{1}{2} => 2*( \frac{x}{6} - 1) = 3 => \frac{2x}{6} - 1 = 3 => \frac{2x-6}{6} = 3 => 2x-6 = 18 => 2x=18+6 => x = \frac{24}{2} => x = 12$

c ) $x+ \frac{x}{3} =8 => \frac{3x+x}{3} = 8 => 3x+x = 24 => 4x = 24 => x = \frac{24}{4} => x = 6$

d ) $\frac{x}{3}-1 = \frac{x}{4} => x = 4*( \frac{x}{3} - 1 ) => x = \frac{4x}{3} - 4 => x = \frac{4x+12}{3} => 3x = 4x+12 => 3x-4x = 12 => (-x = 12)(-1) => x=-12$

 I hope you like it.