Explain he differences between properties of equality and properties of inequality when solving equations and inequalities.

The difference between properties of  equality and properties of inequality that you need to take into account when you are solving equalities and inequalities is the effect that some operations have on the sign.

1) The multiplicative property of equality permits you to multiplicate both members (sides) on an equality times a factor and the equality will remain. But in an inequality, while the factor is positive the inequality will remain but when the factor is negative, the sign of the inequality will change.

2) The same is true about the division property:

3) When you use othe functions like absoulte value and square root you will also need to be attentive of the effect of the function on the sign of the equality,.