Solving Absolute Value Equations – Practice Problems

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Just to refresh your memory, absolute value is the distance of a number from zero. We can also think of it as the magnitude of a number without considering the sign. The absolute value of a number is always a positive number, and the absolute value of zero is zero. You can add, subtract, multiply, and divide with the absolute value of a number. But, how do you solve for the variable of an equation when the variable is part of an expression inside absolute value bars?

The absolute value of the variable expression must be a positive number, but the value of the variable expression inside the bars can be negative or positive. So, if you are trying to determine the value of the variable inside the bars, you must set up two different equations, one positive and the other negative. The answer is one or the other, so the solution can have two different answers.

You will want to verify that both answers work by substituting them back into the corresponding equation. Be careful not to mix up the equations. We use absolute value all the time in the real world. Think about this statement, “Wow, your weight really changed!” This statement can take on two different meanings. Does the statement mean you lost weight or gained weight? It could go either way, just like the value of a variable inside absolute value bars. For more on this, watch the video.

Represent and solve equations with absolute value.


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Exercises in this Practice Problem
What is the temperature at the vacation resort?
Solve the absolute value equation.
Deduce the resulting rates.
Analyze the absolute value equations.
Explain why absolute value equations can have two solutions.
Solve the absolute value equations.