Notice that in both examples, the steps were the same as before. Use this to determine when there are no solutions to an absolute value equation. The absolute value of any number is always positive. This is not possible so there are no possible x-values that make this equation true. Here, we have the absolute value of something is negative. Why? The absolute value of any number is positive. To isolate the absolute value, subtract 3 from both sides.Īt this step, it can be determined that there are no solutions to the equation. We will look more closely at why this happens, but first let’s look at how you might end up with no solutions. Therefore, we will solve two equations without the absolute value: one where the 13 is positive and one where 13 is negative. ExampleĪs mentioned, the absolute value part is already isolated. Whether or not this first step applies or not, you will always have zero, one, or two solutions to any absolute value equation. In this first example, the absolute value part of the equation is already isolated, so only step two will apply.
Let’s try these steps out with some examples! Examples This sounds complicated, but it is only a step or two more than solving the typical linear equation. Then, you will write two equations based on the definition of absolute value (though sometimes, there will end up only being one equation).
When given an absolute value equation, you will first need to isolate the absolute value part of the equation. Steps for solving absolute value equations
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