type of inequalities

ezsmith

Hi, I used to do all this type of inequalities but I have not practice this for almost a year and I have totally forgotten and didn't know why did the sign change.

For example: If it's 3x ≤ 9
The answer: x ≥ 3

Is this right? I have actually forgotten in what circumstances we are suppose to change the inequalities. Input and explanation will be much appreciation. Thanks!

Rikardus

It's actually the other way around, i.e., x <= 3.
You can always test your answer. For example if x = 1, then 3x <= 9. But x is not greater than 3. Thus your answer is wrong.

You only change the inequality when the coefficient is negative ( -x > 0 <=> x < 0).

Mark44

More precisely, the direction of the inequality changes when you multiply both sides of the inequality by a negative number. This includes division, as well, since division by a number is the same as multiplying by the reciprocal of that number.

The direction of the inequality changes if you take the reciprocal of each side. For example, 2 < 3, but 1/2 > 1/3.

Serinety

All of these replies got it right. What helped me when I was learning about inequalities, was to treat it like an equal sign. Then the only additional thing to remember when solving them is to change the direction of the inequality any time you multiply or divide the equation by a negative number.

Also, as was pointed out above. you can always check to make sure the answer makes sense by plugging it back in.

good luck!