Question 116351
Solving inequalities is just the same as solving equations with one very important exception.  Any time you either multiply or divide both sides of the inequality by a negative number, you must reverse the sense of the inequality (less than would become greater than, for example).  


{{{3x+2<=17}}}.  We can add -2 to both sides of the inequality
{{{3x<=15}}}.    We can divide both sides by a positive number, in this case 3
{{{x<=5}}}.      And the problem is solved.


Since we never had to multiply by a negative number, the sense of the inequality never changed.


Let's look at a slightly different problem, just to illustrate the point:


{{{-3x+2<=17}}}.  Again, we can add -2 to both sides
{{{-3x<=15}}}.    But now we have to divide both sides by -3, so the sense of the inequality has to change from less than or equal to greater than or equal.
{{{x>=-5}}}


And that's all you need to know to solve linear single-varible inequalities.


Hope that helps,
John