## Solving Basic Inequalities

### Algebra: Inequalities Help

#### Home | Inequalities menu | Algebra menu

The approach to solving basic inequalities is the same as solving algebra equations. There is just one catch:

**IF THE COEFFICIENT IN FRONT
OF THE X IS NEGATIVE YOU HAVE TO SWITCH THE INEQUALITY DIRECTION WHEN
YOU DIVIDE BY IT.**

Let's do an example.

**Example:** Solve:

-2x - 8 < -14

As usual, we first add 8 to both sides.

-2x - 8 < -14

-2x - 8 + 8 < -14 + 8

-2x < -6

Now we could add 2x to both sides and then add 6 to both sides and then divide both sides by 2 to get the right answer. But why do 3 steps when we can get away with 1? Because the coefficient (which is -2) is negative, all we have to do is switch the inequality when we divide both sides by it and we'll get the same answer as the 3-step approach.

-2x < -6

-2x/-2 > -6/-2

x > 3

So, our solution is x > 3.

## Algebra: Inequalities Help

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