Question

Write an equivalent equation that does not contain fractions.

1) 3/7X+3=1/8_________
X=

2) 1/6X-4=2/9__________
X=

3) 5/8X-10=3/4__________
X=

4) 4/5X-12=3/4___________
X=

Answer 1

`1)\\(3)/(7)x+3=(1)/(8)\ \ \ \ |multiply\ both\ sides\ by\ LCD((3)/(7);\ (1)/(8))=56\\\\56*(3)/(7)x+56*3=56*(1)/(8)\\\\8*3x+168=7\\\\\boxed{\boxed{24x+168=7}}\ \ \ \ |subtract\ 168\ from\ both\ sides\\\\24x=161\ \ \ \ \ |divide\ both\ sides\ by\ 24\\\\\boxed{x=(161)/(24)}`



`2)\\(1)/(6)x-4=(2)/(9)\ \ \ \ |multiply\ both\ sides\ by\ LCD((1)/(6);\ (2)/(9))=18\\\\18*(1)/(6)x-18*4=18*(2)/(9)\\\\3x-72=2*2\\\\\boxed{\boxed{3x-72=4}}\ \ \ \ \ |add\ 72\ to\ both\ sides\\\\3x=76\ \ \ \ \ \ |divide\ both\ sides\ by\ 3\\\\\boxed{x=(76)/(3)}`



`3)\\(5)/(8)x-10=(3)/(4)\ \ \ \ \ |multiply\ both\ sides\ by\ LCD((5)/(8);\ (3)/(4))=8\\\\8*(5)/(8)x-8*10=8*(3)/(4)\\\\5x-80=2*3\\\\\boxed{\boxed{5x-80=6}}\ \ \ \ \ |add\ 80\ to\ both\ sides\\\\5x=86\ \ \ \ \ \ |divide\ both\ sides\ by\ 5\\\\\boxed{x=(86)/(5)}`



`4)\\(4)/(5)x-12=(3)/(4)\ \ \ \ \ \ |multiply\ both\ sides\ by\ LCD((4)/(5);\ (3)/(4))=20\\\\20*(4)/(5)x-20*12=20*(3)/(4)\\\\4*4x-240=5*3\\\\\boxed{\boxed{16x-240=15}}\ \ \ \ \ |add\ 240\ to\ both\ sides\\\\16x=255\ \ \ \ \ |divide\ both\ sides\ by\ 16\\\\\boxed{x=(255)/(16)}`