You can put this solution on YOUR website! 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).
. We can add -2 to both sides of the inequality . We can divide both sides by a positive number, in this case 3 . 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:
. Again, we can add -2 to both sides . 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.
And that's all you need to know to solve linear single-varible inequalities.
