Question 255661
{{{t/3 - t/2 > 3/4}}}

The main problem here is that we need to combine the two fractions on the left hand side of the inequality.  Thus, we need to find the common denominator.  Our two denominators here are 3 and 2, so the lowest common multiple of these is 6.  So our common denominator is 6.  This means that we need to multiply the first fraction by 2/2 and the second fraction by 3/3 to transform them both into fractions with 6 as the denominator.  Thus, we have:

{{{2t/6 - 3t/6 > 3/4}}}

Combining the fractions on the left hand side gives us:

{{{-t/6 > 3/4}}}

Now we are ready to solve for t.  To start, we can multiply both sides of the inequality by 6:

{{{-t > (3/4)*6}}}
{{{-t > 9/2}}}

And last, we need to multiply both sides by -1, remembering that you must flip the inequality when multiplying or dividing by a negative number:

{{{t < -9/2}}}