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What is the effect of multiplying both sides of an inequality by a negative number?
It changes the direction of the inequality.
When solving inequalities using multiplication explain the difference between multiplying each side of the equation by a positive number and multiplying each side of the equation by a negative number?
When you multiply both sides by a negative number the inequality must be flipped over. You do not do that when multiplying by a positive number.
Is it true When dividing by a negative number the direction of the inequality symbol MUST be reversed?
Yes, it is true.
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.
What happenes when you divide or multiply a inequlity by a negative?
Dividing or multiplying by a negative reverts the value to the other side of the number line, thus, the inequality sign must revert as well.
