## Absolute Value Equations: How to solve absolute value equations

Free absolute value equation calculator - solve absolute value equations with all the steps. Type in any equation to get the solution, steps and graph. If you're behind a web filter, please make sure that the domains *winnetttbh.ml and *winnetttbh.ml are unblocked. Solve for x in the following equation. Example 1: Step 1: The absolute value is already isolated. Either 2x-1=+5 or 2x-1=-5 Step 2: Solve the equation 2x-1=+5 Solve the equation 2x-1=-5 The answers are 3 and These answers may not be solutions to the equation. Check the solution x=3 by substituting 3 in the original equation for x. If the.

## Absolute value word problems (video) | Khan Academy

Simpler Harder Special Case. When we take the absolute value of a number, we always end up with a positive number or zero. Whether the input was positive or negative or zerothe output is always positive or zero. This property — that both the positive and the negative become positive — makes solving absolute-value equations a little tricky.

But once you learn the "trick", they're not so bad. Let's start with something simple:. Solving Absolute Value Equations. So then x must be equal to 3 or equal to —3. But how am I supposed to solve this if I don't already know the answer? The "minus" sign in " — x " just indicates that I am changing the sign on x. It does not indicate a negative number.

This distinction is crucial! Whatever the value of x might be, taking the absolute value of x makes it positive. Since x might originally have been positive and might originally have been negative, I must acknowledge this fact when I remove the absolute-value bars. I do this by splitting the equation into two cases. For this exercise, these cases are as follows:. We can, by the way, verify the above solution graphically. For instance:.

If you're wanting to check your answers on a test before you hand it init can be helpful how to solve problems with absolute value plug each side of the original absolute-value equation into your calculator as their own functions; then ask the calculator for the intersection points.

Of course, any solution can also be verified by plugging it back into the original exercise, and confirming that the left-hand side LHS of the equation simplifies to the same value as does the right-hand side RHS of the equation.

For the how to solve problems with absolute value above, here's my check:. If you're ever in doubt about your solution to an equation, try graphing or else try plugging your solution back into the original question.

Checking your work is always okay! The step in the above, where the absolute-value equation was restated in two forms, one with a "plus" and one with a "minus", gives us a handy way to simplify things: When we have isolated the absolute value and go to take off the bars, we can split the equation into two cases; we will signify these cases by placing a "minus" on the opposite side of the equation for one case and a "plus" on the opposite side for the other.

Here's how this works:. The absolute value is isolated on the left-hand side of the equation, so it's already set up for me to split the equation into two cases. To clear the absolute-value bars, I must split the equation into its two possible two cases, how to solve problems with absolute value, one each for if the contents of the absolute-value bars that is, if the "argument" of the absolute value is negative and if it's non-negative that is, if it's how to solve problems with absolute value or zero.

To do this, I create two new equations, how to solve problems with absolute value, where the only difference between then is the sign on the right-hand side. First, I'll do the "minus" case:. Now I need to check my solutions. I'll do this by plugging them back into the original equation, since the grader can't see me checking plots on my graphing calculator.

First, I'll isolate the absolute-value part of the equation; that is, I'll get the absolute-value expression by itself on one side of the "equals" sign, with everything else on the other side:. Now How to solve problems with absolute value clear the absolute-value bars by splitting the equation into its two cases, one for each sign on the argument.

First I'll do the negative case:, how to solve problems with absolute value. The exercise doesn't tell me to check, so I won't. But, if I'd wanted to, I could have plugged "abs 2X—3 —4" and "3" into my calculator as Y1 and Y2, respectivelyand seen that the intersection points were at my x -values. My answer is:.

### Absolute Value Equation Calculator - MathPapa Solve an absolute value equation using the following steps: Get the absolve value expression by itself. Set up two equations and solve them separately. If you're behind a web filter, please make sure that the domains *winnetttbh.ml and *winnetttbh.ml are unblocked. Free absolute value equation calculator - solve absolute value equations with all the steps. Type in any equation to get the solution, steps and graph.