Explicação passo-a-passo:
A)
[tex] \dfrac{x}{3} = \dfrac{8}{12} [/tex]
[tex]12x = 3 \times 8[/tex]
[tex]12x = 24[/tex]
[tex]x = \dfrac{24}{12} [/tex]
x=>2
B)
[tex] \dfrac{2.1}{7} = \dfrac{x}{10} [/tex]
[tex]0.3 = \dfrac{x}{10} [/tex]
[tex]0.3 \times 10 = x[/tex]
[tex]3 = x[/tex]
x=>3
C)
[tex] \dfrac{2}{15} = \dfrac{3}{2x} [/tex]
[tex]15 \times 3 = 2 \times 2x[/tex]
[tex]45 = 4x[/tex]
[tex]4x = 45[/tex]
x=>45/4
D)
[tex] \dfrac{x + 6}{x - 6} = \dfrac{2}{3} [/tex]
[tex]3(x + 6) = 2(x - 6)[/tex]
[tex]3x + 18 = 2x - 12[/tex]
[tex] 3x - 2x = - 12 - 18[/tex]
x=>-30
E)
[tex] \dfrac{1}{5} = \dfrac{x - 6}{x + 1.5} [/tex]
[tex] \dfrac{1}{5} = \dfrac{x - 6}{x + \dfrac{15 {}^{ \div 5} }{10 {}^{ \div 5} } } [/tex]
[tex] \dfrac{1}{5} = \dfrac{x - 6}{x + \dfrac{3}{2} } [/tex]
[tex] \dfrac{1}{5} = \dfrac{x - 6}{ \dfrac{2x + 3}{2} } [/tex]
[tex] \dfrac{1}{5} = \dfrac{(x - 6) \times 2}{2x + 3} [/tex]
[tex] \dfrac{1}{5} = \dfrac{2x - 12}{2x + 3} [/tex]
[tex]2x + 3 = 5(2x - 12)[/tex]
[tex]2x + 3 = 10x - 60[/tex]
[tex]2x - 10x = - 60 - 3[/tex]
[tex] - 8x = - 63( - 1)[/tex]
[tex]8x = 63[/tex]
x=>63/8
F)
[tex] \dfrac{ \dfrac{3}{4} }{ \dfrac{1}{3} } = \dfrac{ \dfrac{1}{2} }{x} [/tex]
[tex] \dfrac{3}{4} \times \dfrac{3}{1} = \dfrac{1}{2} \times \dfrac{1}{x} [/tex]
[tex] \dfrac{9}{4} = \dfrac{1}{2x} [/tex]
[tex]9 \times 2x = 4 \times 1[/tex]
[tex]18x = 4[/tex]
[tex]x = \dfrac{4 {}^{ \div 2} }{18 {}^{ \div 2} } [/tex]
x=>2/9
