Question 133487
Your problem statement is ambigous.  Do you mean {{{(-5-t)/6>=-9}}} or {{{-5-t/6>=-9}}}?



{{{(-5-t)/6>=-9}}}


Multiply both sides by 6:
{{{-5-t>=-54}}}


Add 5 to both sides:
{{{-t>=-49}}}


Finally multiply by -1.  Here is where solving an inequality differs from solving an equation.  If you either multiply or divide by a negative number, you must reverse the sense of the inequality.  Here is a trivial example to illustrate the point:  {{{2<3}}} is clearly a true statement, but if you multiply both sides by -1, you get {{{-2}}} on the left and {{{-3}}} on the right, but you have to change the less than sign to a greater than sign because clearly {{{-2>-3}}}.


{{{t<=49}}}


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{{{-5-t/6>=-9}}}


Add 5 to both sides:
{{{-t/6>=-4}}}


Multiply by 6:
{{{-t>=-24}}}


Multiply by -1 and reverse the sense:
{{{t<=24}}}