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Due to the possibility of an absolute value being either negative or positive, in a simple equation |x = 3|, the x value of the equation must always be set as equal to both of them (x = -3, x = 3). When something is set to 0, you’re solving for the x-intercepts, otherwise known as the solutions.
1. To start solving the equation, you must first isolate the absolute value to one side.
2. Next, you much see if the absolute value set is equal to a negative. If the absolute value does happen to be equal to a negative, then the equation has no solution. This is due to the fact that it’s impossible to have a negative distance from 0.
3. After isolating the absolute value, you remove the absolute value signs and solve the equation. Then, you must make the integers that were moved away from the absolute value negative, and solve the equation again, giving you both x-intercepts. If there is a variable on the side opposite from the absolute value, then you must put a parentheses around the whole equation on that side, then put a negative symbol before the parentheses.
4. After that, you would solve the equation normally.
5. Finally, after solving, you must check the equation by plugging in the answers that you got for the x-value and see if they cancel out. If one of the solutions is negative (ex. x = -1), then the solution will not work. This is called an extraneous solution. An extraneous solution is a result that works mathematically but does not satisfy the original equation.

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When solving the absolute value equations, you want to follow five main steps. These steps will help you determine when the answer is logical, correct, or incorrect. The first step would be to:
1. Isolate the absolute value on one side the equation this meaning that if you have any numbers outside of the absolute value equation you would want to move them to the other side. The second rule isL
2. Determine if the absolute value is set equal to a negative. In the case that the absolute value is set equal to a negative the answer will be no solution because an absolute value cannot be set to a negative number. The third step, assuming that it is not set to a negative number, would be:
3. Set the quantity inside the absolute value equal to + and - the quantity on the other side of the equation. This means set the equations to be both negative and positive. After this the next step would be to.
4. Solve the equations when they are both negative and positive.
Finally the last step would be:
5. Check
When checking you may run into an issue called an extraneous set. This term means that the work is mathematically correct however, if you check your equation and the answer turns out negative it would not satisfy the idea of an absolute value equation.  In the end, these main steps will help you in solving absolute value equations.

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Problem #2

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When solving the absolute value equations you first want to make sure you isolate the absolute value in the equation. Example of this could be |5x-1|+4=7you will subtract 4 from 7 and get 3. Your new equation would be |5x-1|=3.If you have an absolute equation that is written like 4|5x-1|=3you would divide both sides by 4 and then get |5x-1|=34.You will then look to see if the absolute value is equal to a negative number and if no then you will proceed on with the problem. Next you're going to set the number on the other side of the absolute value to a positive and then another equation with it negative like this |5x-1|=3 and |5x-1|=-3.Next remove your bars from the absolute value and solve with regular algebra. You then will get the answers y=45 and y=-25.You then want to go back and check you answer by plugging in your answer for x in both problems |5(45)-1|+4=7 and |5(-25)-1|+4=7.Then you see if the answer matches and if you end up with 7=7 for both then you are good.

When solving absolute value equations there a few things you need to remember. The first thing is after you isolate the absolute value and the equation is equal to a negative you need to stop because you can not have a negative distance from 0. An example of this would be |5x-3|=-9 your answer would be either no solution or you could write a 0 with a line through it like this . Also when you are done solving the problem and you check it over and it comes out like this 5=-13it is called an extraneous solution because the answer to absolute value equation cannot be negative.
Problem #1

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In this video I learned how to solve absolute values equations. While watch the video I learned that there are 5 steps.  I will be using the equation |2x-4|+8=16 The first step is to isolate the absolute value to one side by subtracting 8 from 16 then since you just subtracted your new equation would be 2x-4=8.Then you have to make sure  that the absolute value equation is not set to a negative number. If it is set to a negative number you will receive a no solution equation. The third step would be to add or subtract the equation in side the absolute value from the answer, so that the second equation is negative. After that you have to remove the brackets from the absolute value so that you can solve. From there you should get one negative answer and one positive answer. From there you want to do the last step which is the "Check" part. The Check part is when you plug in your x with the variable you found to see if the variable is the right one to the equation. ones you equation has this --> #=# (SAME NUMBER THOUGH) you know the solve the problem correctly.

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 Roshana stevens                      To solve an absolute value it takes 5 easy steps. Using the example 2x-2+4=8 the first step would be to isolate the absolute value to one side by subtracting 4 from 8, then you would get the equation 2x-2=4. The next step would be to ask  yourself if the abs value is set to a negative, in this case it is not so we can move on (of it did you would have to make sure the absolute value could equal a negative and if not the answer would be “no solution”). Step 3 would be to add or subtract the quantity inside the absolute value from the answer and create the second equation making the second answer negative. You would add the 2 to the 4 creating the new equation of 2x=6 and 2x=-6. Then you would solve both equations getting the answer 3 and -3. The last step is to plug it back in to make sure you have got the right answers.

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 Roshana stevens                      To solve an absolute value it takes 5 easy steps. Using the example 2x-2+4=8 the first step would be to isolate the absolute value to one side by subtracting 4 from 8, then you would get the equation 2x-2=4. The next step would be to ask  yourself if the abs value is set to a negative, in this case it is not so we can move on (of it did you would have to make sure the absolute value could equal a negative and if not the answer would be “no solution”). Step 3 would be to add or subtract the quantity inside the absolute value from the answer and create the second equation making the second answer negative. You would add the 2 to the 4 creating the new equation of 2x=6 and 2x=-6. Then you would solve both equations getting the answer 3 and -3. The last step is to plug it back in to make sure you have got the right answers.

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In this video I learned how to solve absolute value equations. The first step to solving absolute value equations is by isolating the absolute value on one side of the equation. Then you have to make sure  that the absolute value equation is not set equal to a negative number. If it is, you automatically know that the equation = no solution. Once you have determined that the equation has been set equal to a positive number you then have to set the numbers inside the absolute value positive. The only time you would not make them positive is if there was a negative sign on the outside of the absolute value. Once you have gotten rid of the absolute value you simply solve the equation algebraically to find your answer for x. Once you have found the answer you can check your work by plugging the x value you got back into the equation to make sure that the output is correct.

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In this video I learned how to solve absolute value equations. There are four steps for how you do this. First, you need to make sure your absolute value is on one side of the equation. If once you do this you see that your absolute value is equal to a negative number you know that their is no solution, because an absolute value can never equal a negative number. When you absolute value equation is equal to a positive number you solve for x and you change the other equation to be equal to a negative number. From here you solve both equations for x. In conclusion, you can check your answer by plugging your x values back into the equation to see if the output is true.
Examples:

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An x-intercept for an absolute value function are two points on the absolute value function, where it intersects the x-axis. Therefore, when y equals zero these will be the values for x. First you solve algebraically for x. Then, I set the absolute value side equal to the negative of the right side of the equation which does not contain absolute value signs, and solve algebraically. You can check your x-intercepts by plugging them both individually into the original equation. If both sides are equal, then that those values for x are solutions. If neither of the values for x work then, there is no solution. If one of the values for x works, then that is the solution. The other value for x would be considered an extraneous solution meaning that it is not a solution.If there are variables on both sides of the equations you make the side that does not contain the absolute value signs negative, by putting it in parentheses and putting the negative sign outside of the parenthesis, which you then distribute. The slope which is in front of the absolute value signs is divided on both sides of the equation before you can solve for x.For example to solve the equation,  y= 2|x-6|-4 you first set y equal to zero. Then you can isolate four on one side by adding four to both sides so the equation should look like this,  4= 2|x-6|. Next, you divide by 2 on both sides of the equation, meaning that the function should be 2= |x-6| . Then, you can solve for x, which in this case would be x=8. Now, you set  -4= 2|x-6| because you need to know where it hits the x-axis on the other side of the vertex. You can divide by 2 on both sides so the equation would now be -2= |x-6|. Then you can solve for x which would be x=4. These two values that equal x are the x-intercepts, and I can check them by plugging them back into the original equation. In this case both sides of the equations equal each other meaning that my x-intercepts are correct.

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An x-intercept for an absolute value function are two points on the absolute value function, where it intersects the x-axis. Therefore, when y equals zero these will be the values for x. First you solve algebraically for x. Then, I set the absolute value side equal to the negative of the right side of the equation which does not contain absolute value signs, and solve algebraically. You can check your x-intercepts by plugging them both individually into the original equation. If both sides are equal, then that those values for x are solutions. If neither of the values for x work then, there is no solution. If one of the values for x works, then that is the solution. The other value for x would be considered an extraneous solution meaning that it is not a solution.If there are variables on both sides of the equations you make the side that does not contain the absolute value signs negative, by putting it in parentheses and putting the negative sign outside of the parenthesis, which you then distribute. The slope which is in front of the absolute value signs is divided on both sides of the equation before you can solve for x.For example to solve the equation,  y= 2|x-6|-4 you first set y equal to zero. Then you can isolate four on one side by adding four to both sides so the equation should look like this,  4= 2|x-6|. Next, you divide by 2 on both sides of the equation, meaning that the function should be 2= |x-6| . Then, you can solve for x, which in this case would be x=8. Now, you set  -4= 2|x-6| because you need to know where it hits the x-axis on the other side of the vertex. You can divide by 2 on both sides so the equation would now be -2= |x-6|. Then you can solve for x which would be x=4. These two values that equal x are the x-intercepts, and I can check them by plugging them back into the original equation. In this case both sides of the equations equal each other meaning that my x-intercepts are correct.

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In this video I learned how to solve absolute value equations. The first step is to isolate or separate so it is alone the absolute value on one side of the equation. Next, you ask yourself is the absolute value set equal to a negative if this is true then the answer is no solution because an absolute value can never equal a negative number. If it is set equal to a positive number then you set the quantity inside the absolute value equal to a negative and positive quantity on the other side of the equation and solve for x in both equations. Finally, you plug your quantities equal to x back into the equations to set if they create a true statement in order to check. If one or both quantities equal to x makes the statement true then you have an extraneous statement meaning you have a solution that works mathematically but does not satisfy the original equation. Here are some examples of solving absolute value equation:

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Your first task will be to review the attached video link on "solving absolute value equations". Take notes as you watch the video.  When done, click anywhere on the screen and add a brief summary of what you learned.  To support your understanding create two additional examples of your own and solve them.  Post them within the same post.

To begin, click on the video below.