How To Solve Absolute Value Equations

TL;DR

Learn how to solve absolute value equations by considering both positive and negative solutions.

Transcript

in this video we're going to focus on solving absolute value equations now i recommend that you watch this video to the end because the problems they're going to start off easy but over time they're going to get harder and harder so stay tuned let's start with some basics let's say if we have the absolute value of x and it's equal to 9 what is x eq... Read More

Key Insights

• ❎ Absolute value equations involve considering both positive and negative solutions for a variable.
• 🟰 The absolute value of a negative number is equal to its positive value.
• 😑 When solving absolute value equations, set up two equations by separating the expression inside the absolute value into positive and negative values.
• ✅ It is crucial to check the solutions by substituting them back into the original equation to ensure their validity.
• 🍳 Numbers outside of the absolute value should be simplified before breaking up the equation into two equations.
• 🟰 Some absolute value equations may have no solutions if the absolute value of a number cannot equal a negative value.
• ❓ Solutions to absolute value equations can be decimal or fractional values.

Questions & Answers

Q: What is the general approach for solving absolute value equations?

To solve an absolute value equation, set up two equations by considering both positive and negative values for the expression inside the absolute value. Solve each equation separately to find the possible solutions.

Q: Can a negative number be a solution to an absolute value equation?

Yes, when solving absolute value equations, both positive and negative values can be solutions. This is because the absolute value of a negative number is equal to its positive value.

Q: What should you do if there are numbers outside of the absolute value in an equation?

If there are numbers outside of the absolute value in an equation, do not immediately set up two equations. Simplify the equation first before breaking it up into two equations.

Q: Why is it necessary to check the solutions of an absolute value equation?

It is important to check the solutions by substituting them back into the original equation to ensure they are valid and satisfy the equation.

Summary & Key Takeaways

• Absolute value equations involve finding values for a variable that satisfy the equation, considering both positive and negative solutions.

• To solve an absolute value equation, set up two equations by separating the expression inside the absolute value into positive and negative values.

• Solve each equation separately, and the solutions will be the values of the variable that make the equation true.

• It is important to check the solutions by substituting them back into the original equation to ensure they are valid.