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Because when you fit in the variables, it wouldn't be true. therefore, you have to flip the inequality sign
For example,
3 > 2 True
3(-2) > 2(-2)
-6 > -4 False
If you change the direction of the inequality symbol, in the same time that you multiply by a negative number, then you find a true statement.
3 > 2 True
3(-2) < 2(-2)
-6 < -4 True
This is because the greater the absolute value of a negative number, the lesser it is, while the opposite is true for a positive number. When you multiply by a negative, a very large number becomes very small, or the opposite.
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Do you flip the inequality when adding and subtracting?
No. Only flip the inequality when multiplying or dividing by a negative number.
When you divide both sides of an inequality by a negative number you need to blank the inequality symbol?
Flip. You need to reverse the inequality when multiplying or dividing by a negative. -2x < 10 (-1)*(-2x) < (-1)*10 2x > -10 x > -5
When you divide both sides of any inequality by a negative number you need to what the inequality symbol?
Flip it around
When the inequality is multiplied both sides by a positive number what happens?
Nothing, you proceed as if the < or > was an =. If you're multiplying or dividing both sides by a negative, you flip the sign. e.g. < would go to >
Why must you flip the inequality symbol when you divide by a negative number?
For the same reason you must flip it when you multiply by a negative number. An example should suffice. 2 < 3 If you multiply by -1, without switching the sign, you get: -2 < -3, which is wrong. Actually, -2 > -3. Look at a number line if you are not sure about this - numbers to the left are less than numbers further to the right. Dividing by a negative number is the same as multiplying by the reciprocal, which in this case is also negative. These signs are strictly the "Greater than" and "Less than" signs. The inequality sign is an = with a / stroke through it. If you divide an inequality by -1 it remains an inequality.
