properties+of+order

The properties of order show the relative order of numbers or equations. The symbols of the properties of order would be the < (less than) or > (greater than). These properties destinguish what part of the equation to solve and when to solve it. "Comparison axiom: If a and b are real numbers, then one and only one of the following statements is true:a > b, a = b, a < b.

Consider the inequality The basic strategy for inequalities and equations is the same: isolate //x// on one side, and put the "other stuff" on the other side. Following this strategy, let's move +5 to the right side. We accomplish this by subtracting 5 on both sides to obtain after simplification we obtain Once we divide by +2 on both sides (Rule 3a), we have succeeded in isolating //x// on the left: or simplified

Find all solutions of the inequality Let's start by moving the ``5'' to the right side by subtracting 5 on both sides: or simplified, How do we get rid of the ``-'' sign in front of //x//? Just multiply by (-1) on both sides changing " " to "  " along the way: or simplified

Solve the inequality Let us simplify first: There is more than one route to proceed; let's take this one: subtract 2//x// on both sides. and simplify: Next, subtract 9 on both sides: simplify to obtain Then, divide by 4: and simplify again: It looks nicer, if we switch sides. In interval notation, the set of solutions looks like this:. these examples came from sosmath.com

Some helpful websites would be: http://www.sosmath.com/algebra/inequalities/ineq01/ineq01.html and http://www.math.com/school/subject2/lessons/S2U1L2GL.html

i could not get the URL but here is a link to a video on the topic: http://images.google.com/imgres?imgurl=http://www.stevetoner.com/lectures/IMAG006A.JPG&imgrefurl=http://www.stevetoner.com/lectures.html&usg=__0LianCWkxQYFnG8_QhZ8Fsxt2VQ=&h=480&w=720&sz=36&hl=en&start=8&um=1&tbnid=gnr6Bw07j1H7FM:&tbnh=93&tbnw=140&prev=/images%3Fq%3Dproperties%2Bof%2Border%2Bfor%2Bmath%26um%3D1%26hl%3Den

1. x = 7 < -2

2. -8 > y +9

3. 5a < -30

4. -4d < -36

5. 15<-3c