Solving Basic Inequalities

Algebra: Inequalities Help


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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.

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Algebra: Inequalities Help

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