# Solving absolute value equations and Inequalities; how anyone can learn

# Solving Absolute Value Equations

Knowing the absolute value of a number is essential as we investigate solving absolute value equations. So

what do we need to know about the absolute value of a number that is going to be helpful for us?

Well we need to know that $abs[9]=9$ and $abs[-9]=9$ This tells us that if we have an equation such as $abs(x)=9$ then there are two possible solutions $9$ and $-9$. When solving absolute value equations there are 4 steps we will follow

- Isolate the absolute value symbol by using inverse operations and properties of equality.
- Create two cases by setting the quantity of the absolute value equal to the positive and negative quantity of the other side of the equation
- Solve each equation using inverse operations
- Check your answer for extraneous solutions by plugging in your solution back into the original absolute value equation

In the next four videos we will explore how to use this process

## Solving One Step Absolute Value Equations

The main point to drive home with solving absolute value equations is to set up your two cases. However before you can set up your two cases and negate one, you must have the absolute value symbol isolated on one side of the equal sign. Below we will work through problems where this is the case.

## Solving Two-Step Absolute Value Equations

## Solving Absolute Value Equations by isolating your ABS sign first

Coming Soon.. Check my YouTube channel for examples

I do have to warn you. Not every problem is going to be so straight forward with both solutions. You should always go back and check your solution for the previous problems but for what we are to do next it is a must to check your answer.

Why?

Well in the last set of examples we are going to solve absolute value equations where there is a variable on both sides. We will still use the same process as before but when creating two cases with a variable on both sides we have to check for extraneous solutions. To do that we will plug in both solutions back into our original equation to make sure they make the equation true. If so they are a solution. If not they are what we called extraneous and not apart of the solution.

See the video below for yourself

## Solving Absolute Value Equations with Extraneous Solutions

## Solving Absolute Value Equations with Extraneous Solutions More Examples

Coming Soon….check my YouTube channel for examples

I hope these three video have will help you solving absolute value equations for more help CLICK HERE

# Solving Absolute Value Inequalities

When Solving Absolute Value Inequalities the process is very similar to solving equations however there are a couple of differences I will show you in the below videos. The general process goes like this

- Isolate your absolute value symbol(Remember if you multiply of divide by a negative number you have to switch the sign)
- Create your two cases (Remember when creating case #2 with negation you have to flip the sign) For less than or less than or equal to you have a conjunction “and” inequality. For greater than or greater than or equal to you have a conjunction “or” inequality
- Solve the compound inequality
- Graph the compound inequality on the same numberline