Question 447427
{{{3/2x - 6/x = 9}}}
==> Find the least common denominator (LCD) of 2x and x. It is 2x.
==> Multiply everything in the equation by this LCD of 2x: {{{(2x)(3/2x) - (2x)(6/x) = (2x)(9)}}}
==> Simplify. Notice that the 2x cancels out the /2x in {{{3/2x}}} and the x cancels out the /x in {{{6/x}}}: 3 - 12 = 18x
==> Combine like terms: -9 = 18x
==> Divide both sides by 18: {{{-9/18 = x}}}
==> Simplify: {{{-1/2 = x}}}
*** Therefore, x is {{{-1/2}}}
==> You can check your answer by plugging this value of x back into the original equation.
==>{{{3/(2(-1/2)) - 6/(-1/2) = 9}}}
==> Simplify. Notice that the 2 cancels out the /2 in {{{-1/2}}}, and that the - in the -6 and - in the {{{-1/2}}} cancel each other out to become positive. Also, {{{6/(1/2) = 6*2}}}: {{{3/-1 + 12 = 9}}}
==> Simplify: -3 + 12 = 9
==> Combine like terms: 9 = 9
*** Therefore, x = {{{-1/2}}}