Question

Write an equivalent equation that does not contain fractions.

Answer 1

$1)\\\frac{3}{7}x+3=\frac{1}{8}\ \ \ \ |multiply\ both\ sides\ by\ LCD(\frac{3}{7};\ \frac{1}{8})=56\\\\56\times\frac{3}{7}x+56\times3=56\times\frac{1}{8}\\\\8\times3x+168=7\\\\\boxed{\boxed{24x+168=7}}\ \ \ \ |subtract\ 168\ from\ both\ sides\\\\24x=161\ \ \ \ \ |divide\ both\ sides\ by\ 24\\\\\boxed{x=\frac{161}{24}}$


$2)\\\frac{1}{6}x-4=\frac{2}{9}\ \ \ \ |multiply\ both\ sides\ by\ LCD(\frac{1}{6};\ \frac{2}{9})=18\\\\18\times\frac{1}{6}x-18\times4=18\times\frac{2}{9}\\\\3x-72=2\times2\\\\\boxed{\boxed{3x-72=4}}\ \ \ \ \ |add\ 72\ to\ both\ sides\\\\3x=76\ \ \ \ \ \ |divide\ both\ sides\ by\ 3\\\\\boxed{x=\frac{76}{3}}$


$3)\\\frac{5}{8}x-10=\frac{3}{4}\ \ \ \ \ |multiply\ both\ sides\ by\ LCD(\frac{5}{8};\ \frac{3}{4})=8\\\\8\times\frac{5}{8}x-8\times10=8\times\frac{3}{4}\\\\5x-80=2\times3\\\\\boxed{\boxed{5x-80=6}}\ \ \ \ \ |add\ 80\ to\ both\ sides\\\\5x=86\ \ \ \ \ \ |divide\ both\ sides\ by\ 5\\\\\boxed{x=\frac{86}{5}}$


$4)\\\frac{4}{5}x-12=\frac{3}{4}\ \ \ \ \ \ |multiply\ both\ sides\ by\ LCD(\frac{4}{5};\ \frac{3}{4})=20\\\\20\times\frac{4}{5}x-20\times12=20\times\frac{3}{4}\\\\4\times4x-240=5\times3\\\\\boxed{\boxed{16x-240=15}}\ \ \ \ \ |add\ 240\ to\ both\ sides\\\\16x=255\ \ \ \ \ |divide\ both\ sides\ by\ 16\\\\\boxed{x=\frac{255}{16}}$