# How to write an absolute value equation with given solutions catalog

Because the original equation contained an absolute value, you're left with two relationships between x and y that are equally true. Even the best athletes and musicians had help along the way and lots of practice, practice, practice, to get good at their sport or instrument. When you take the absolute value of a number, the result is always positive, even if the number itself is negative.

To solve this, you have to set up two equalities and solve each separately. Plug in known values to determine which solution is correct, then rewrite the equation without absolute value brackets. Math works just like anything else, if you want to get good at it, then you need to practice it.

At the link you will find the answer as well as any steps that went into finding that answer. If you already know the solution, you can tell immediately whether the number inside the absolute value brackets is positive or negative, and you can drop the absolute value brackets.

Equation 2 is the correct one. Once you apply the definition and set it up without the absolute value, you just solve the linear equation as shown in Tutorial Linear Equations in One Variable. If you plot the above two equations on a graph, they will both be straight lines that intersect the origin. Writing an Equation with a Known Solution If you have values for x and y for the above example, you can determine which of the two possible relationships between x and y is true, and this tells you whether the expression in the absolute value brackets is positive or negative.

There is only one solution to this absolute value equation: 2.

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