1B+Linear+Inequalities

=HOW TO FIND A LINEAR INEQUALITY=


 * 1) What is a Linear Inequality?
 * 2) And Or Statements
 * 3) Graphing Linear Inequalities with One Variable
 * 4) Linear Inequalities with Two Variables
 * 5) Graphing Linear Inequalities With two Variables

Definition
-A Inequality is an equation that is not equal.

Why are equations important in real life?

This can help sort out how your options are, such as shoe size. You can know whether what shoe size you can wear without going to big or to small but just right.

Before We get Started:
These are some symbols you should know before writing or solving an equation. When writing a linear inequality, you have to determine whether the numbers are:

greater than > less than < equal to = greater than or equal to ≥ less than or equal to ≤ not equal to ≠ __Example 1__ ** 4 > 2 can be read as 4 is greater than 2.
 * 

Sometimes variables are incorporated into the equations.

   ** __Example 2__ **

2x+5≠10

Now the first thing to do in any equation is to get x by itself. So you subtract 5 from both sides 2x+5 ≠ 10 -5 ≠ -5 __2x__ ≠ __5__ 2 2 x ≠ 2.5 Now we found the equation which reads x is not equal to 2.5.

If you need more Help just go to this [|link] for more info and problems to help you.

 =**And + Or Statements**=


 * And**= means in between

__**Example 5 :** __ I read at least 6 hours a day //**AND**// no more than 15.


 * Or**= means more or less, no in between

__**Example 6:** __ Best time to call me would be before 7am or after 9pm. That would be the best time, not //**IN BETWEEN**// those to times.

 =Graphing Linear Inequalities in One Variable=

When drawing or graphing an inequality equation you have to know how it works.

__**Example 3 **__ If the equation says x__<__ 3.... Another way to read that would be x is less than or equal to 3.

You can draw it like this: You should always remember to fill in your circle when it is either greater then or equal to or less then or equal to.

__Example 4__ Here is an example where you don't shade in the circle.

 = = =Linear Inequalities with Two Variables=

Definition: A Linear Inequality with two variables is an inequality that has one of these ways of writing it:

1. Ax + By < C 2. Ax + By > C 3. Ax + By is less than or equal to C 4. Ax + By is greater than or equal to C

In each of the examples, the two variables are x and y. A,B, and C are constants (numbers) that are usually given to you.

An example of this inequality is 4x + 5y < 15.

**Graphing Linear Inequalities with Two Variables:**
Explanation:

First, you must begin by solving an equation. For an example 2y + 4x ≤ 10. In order to solve 2y + 4x ≤ 10 you must subtract 4x from both sides of the equation and then divide both sides by 2. You then end up with y ≤ -2x +5.

This inequality can be rewritten as y < -2x + 5 or y = -2x + 5.

We know how to graph y = -2x + 5. With this you can identify the slope as -2 or -2/1 and 5 as the y-intercept. Next, you must plot your slope and y-intercept on your graph. After connected the dots and making a straight line on your graph, you want to find the answers to y < -2x + 5. The answers are either above or below the line y = -2x + 5.

We'll do a test to see if (0,3) is a solution to our inequality. To test if (0, 3) is a solution, you must replace your x and y variables with 0 to get a true or false statement. 3 ≤ -2* 0 + 5 3≤ 5 3 ≤ 5 (0,3) is a solution. Therefore, you must shade below the line.