As with algebraic equations, the solution to an inequality is a value that makes the inequality true.

     You can solve inequalities in the same way you can solve equations, by adding a positive or negative number to both sides of the inequality or by multiplying or dividing both sides of the inequality by any positive number.

Note: If you multiply or divide both sides of an inequality by a negative number, reverse the direction of the inequality sign!

     Solving an inequality is very similar to solving an equation except for one important thing you must remember!

     When you multiply or divide each side of the inequality by a negative number, you have to reverse the inequality symbol! Let's try an example:

-3x > 18

     Since this inequality involves multiplication, you must use the inverse, or division, to solve it. We'll divide both sides by –3 in order to leave x alone on the left side.

-3x > 18

  -3     -3

When we simplify, because we're dividing by a negative number, we have to remember to reverse the symbol. This shows "x is less than –6," not "x is greater than –6."

x < -6   

Notice that we reversed the direction of the inequality sign

You can check to see if the answer is correct by substituting for x.

-3x > 18
-3(-7) > 21
21 > 18 Correct!

Since our substitution gave a true result the solution is correct.