Inequalities

Inequalities
-Range of values for a solution.

Solving a compound linear inequality:

Example:

2<3x+5<2x+11

A solution of 2<3x+5<2x+11 is any number that is a solution of both of the following inequalities.
2<3x+5 and 3x+5 <2x +11
each of these inequalities can be solved by the principles listed above.

2 - 5 <3x       3x - 2x< 11- 5
-3<3x             x<6
-1<x

the solutions are all real numbers that satisfy both -1<x and x<6, that is -1<x<6. Therefore, the solutions are the numbers in the interval [-1,6).

Example:
 4 < 3-5x<18
When a variable appears only in the middle of a compound inequality the process can be streamlines by performing any operation on each part of the compound inequality.
4<3-5x<18
1<-5x<15
-1/5> x > -3
Intervals are usually written from the smaller to the larger, so the solution to the compound inequality is -3<x<-1/5
The solution of a compound inequality is the interval (-3,-1/5)

Kahn Academy:
http://www.khanacademy.org/video/algebra--solving-inequalities?playlist=Algebra
http://www.khanacademy.org/video/quadratic-inequalities?playlist=Algebra