Help with "and" statements in inequalities.?

Question

I understand the "or" statements, but I'm not sure if I'm supposed to do the whole thing with switching the inequality sign and changing the number at one side of the inequality to a negative. I have a test tomorrow and still don't understand. Can anybody explain to me what to do?

Answer 1

An "and" means that two things both need to be true.

If the inequality is in one variable, there are three main cases, namely:

1. The inequalities contradict each other. For example, x < 1 AND x > 3. There are no solutions to that.

2. The inequalities are somewhat redundant. For example, x < 1 AND x < 3 has exactly the same solutions as x < 3.

3. The inequalities confined the variable to an interval with both an upper and lower bound. For example, x > 1 AND x < 3 marks out a region on the number line that is 2 units long.

All inequalities in one variable can be reduced to one of four cases:

A. x is less than (a specific constant)
B. x is less than or equal to (a specific constant)
C. x is greater than (a specific constant)
D. x is greater than or equal to (a specific constant)

Make those reductions FIRST, and worry about ANDs or ORs only AFTERWARDS.

Answer 2

http://regentsprep.org/Regents/mathb/7d7/Linequal.htm

hope that helps...i had a test on that weeks ago... it was hell! good luck!!!