Відповідь:

5

Покрокове пояснення:

[tex]\frac{0,125x}{(\frac{19}{24} -\frac{21}{40} )*8\frac{7}{16} } =\frac{(1\frac{28}{63} -\frac{17}{21} )*0.7}{0.675*2.4-0.02}[/tex]

Сделаем по порядку (по действиям):

Упростим левую сторону:

1) [tex]\frac{19}{24} -\frac{21}{40} =\frac{19*5}{24*5} -\frac{21*3}{40*3}=\frac{95}{120} -\frac{63}{120}=\frac{32}{120} =\frac{4}{15}[/tex]

2) [tex](\frac{19}{24} -\frac{21}{40} )*8\frac{7}{16} =\frac{4}{15} *8\frac{7}{16} =\frac{4}{15}*\frac{8*16+7}{16} =\frac{4}{15}*\frac{135}{16}=\frac{135}{15} *\frac{4}{16} =9*\frac{1}{4} =2.25[/tex]

3) [tex]\frac{0,125x}{(\frac{19}{24} -\frac{21}{40} )*8\frac{7}{16} } =\frac{0.125x}{2.25} =0.125x:2.25=\frac{1}{8} x:\frac{9}{4} =\frac{1}{8} x*\frac{4}{9} =\frac{x}{18}[/tex]

Теперь с правой стороны упростим:

4) [tex]1\frac{28}{63} -\frac{17}{21} =\frac{63+28}{63} -\frac{17*3}{21*3}=\frac{91}{63} -\frac{51}{63} =\frac{40}{63}[/tex]

5) [tex](1\frac{28}{63} -\frac{17}{21} )*0.7=\frac{40}{63} *0.7=\frac{40}{63} *\frac{7}{10}=\frac{40}{10} *\frac{7}{63} =4*\frac{1}{9} =\frac{4}{9}[/tex]

6) [tex]0.675*2.4=\frac{675}{1000} *\frac{24}{10} =\frac{675:25}{1000:25} *\frac{24:2}{10:2} =\frac{27}{40}* \frac{12}{5} =\frac{27}{5} *\frac{12}{40} =\frac{27}{5} *\frac{3}{10} =\frac{81}{50}[/tex]

7) [tex]0.675*2.4-0.02=\frac{81}{50} -\frac{2}{100} =\frac{81}{50} -\frac{2:2}{100:2}=\frac{81}{50} -\frac{1}{50} =\frac{80}{50}=\frac{8}{5}[/tex]

8) [tex]\frac{(1\frac{28}{63} -\frac{17}{21} )*0.7}{0.675*2.4-0.02}=\frac{4}{9} :\frac{8}{5} =\frac{4}{9} *\frac{5}{8} =\frac{20}{72}[/tex]

Теперь решим упрощенное уравнение:

[tex]\frac{x}{18} =\frac{20}{72}\\72x=20*18\\72x=360\\x=360:72\\x=5[/tex]