Inequality problems?

Question

I have a math test and it is on inequalities and absolute values like there is greater than or equal and all these things and rules so the teacher says u need to graph then find solution but like there are so many different kinds. Help any websites for all the rules or stuff

Answer 1

The most important thing about inequalities is that you can basically treat them like equalities EXCEPT that when you multiply by a negative number, you must reverse the sign.

For example, -x = 2 can be changed to x = -2, no problem.
But -x < 2 must become x > -2, because you are multiplying by negative 1.

Let's say you have a formula y < 2x + 3.

First draw the line y = 2x + 3. It's got a slope of 2 and a y-intercept of (0,3). Draw it as a hashed line, because of the < sign. If it were a <= sign, you would draw it solid.

Now, is y > or <. It's <, so shade in the area under the line. If it said y > 2x + 3, you'd shade in the area above the line.

For absolute values, solve the problem once as a positive and once as a negative.

| x + 3 | > 10
(x + 3) > 10 and -(x + 3) > 10
x + 3 > 10 and -x - 3 > 10
x > 7 and -x > 13
x > 7 and x < -13 (switch signs when multiplying by a negative)

To graph that, draw vertical lines at x = 7 and at x = -13. Your lines are going to be hashed, because of the > and not the => sign. Since x > 7, shade to the right of the x = 7 line. Since x < -13, shade to the left of the x = -13 line.

Answer 2

Some good interactive activities

http://www.ltcconline.net/greenl/java/BasicAlgebra/AbsoluteValues/AbsoluteValues.html
http://www.ronblond.com/M11/LinIne/index.html