# 1 5 solving inequalities worksheet answers algebra 2

## Algebra 2 Solving Inequalities Lesson 1-5 Part 1.

How to Solve Inequalities (NancyPi)

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There are many opportunities for mistakes with absolute-value inequalities, so let's cover this topic slowly and look at some helpful pictures along the way. When we're done, I hope you will have a good picture in your head of what is going on, so you won't make some of the more common errors. Once you catch on to how these inequalities work, this stuff really isn't so bad. Absolute Value Inequalities. This means that their absolute values will both be 2 ; that is, we have:.

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The half-plane that is a solution to the inequality is usually shaded. Share on Facebook. Search Pre-Algebra All courses.

In the final two sections of this chapter we want to discuss solving equations and inequalities that contain absolute values. Before solving however, we should first have a brief discussion of just what absolute value is. There are two ways to define absolute value. There is a geometric definition and a mathematical definition. We will look at both.

Solving Inequalities notation. Then, graph the solution set on a number line. _>2 (z _ 3. ~,-~}. 5. 3x ~ -9 {;;1 Glencoe Algebra 2. 2:<:< .
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Solving inequalities is not so different from solving regular equations. Before all that, let us define the different inequality signs:. Inequalities are best thought of as representing different regions on a number line:. Most linear inequalities can be solved just the same as linear equations: Addition and subtraction of any number positive or negative can be done to the expression on either side of the inequality without changing the inequality itself. In other words, it would be the same as in any ordinary equation. Observe that the above is solved in the same was as solving ordinary equations.

Now that you've studied the many examples for solving inequalities , are you ready for some practice problems? Now you get a chance to solve a few on your own. Try each of the practice problems on your own before checking your answer below. If you get stuck, go back and review the examples problems. Directions: Solve each inequality and graph the solution. Click here to print out number lines for your practice. This problem looked tricky only because I had to first simplify the right hand side.

Are you ready to dive into our solving inequalities unit? Let's do a very quick review of inequality basics that you probably first learned about in second grade. Always remember that inequalities do not have just one solution. There are always multiple solutions! Think about the following inequality:.

## Absolute-Value Inequalities

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Steps for Graphing Your Solution to the Inequality

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