Absolute value equations example 1 | Linear equations | Algebra I | Khan Academy

TL;DR

When solving absolute value equations, remember that the absolute value of a number can be equal to either the positive or negative value of that number.

Transcript

Solve for x, and we have the absolute value of 2x minus 5 is equal to 11. Now, the big, I guess, insight you need to have whenever you have an absolute value equation like this is just to remember, if I have the absolute value of a is equal to 11, what do we know about a? That means that a is equal to 11, or what else could a be? Well, it could be ... Read More

Key Insights

• 😑 Absolute value equations involve considering both the positive and negative values of the absolute value expression.
• 🟰 Solving absolute value equations requires setting the expression inside the absolute value sign equal to both the positive and negative values of the given absolute value.
• ❓ The solutions to an absolute value equation may or may not satisfy additional constraints given in the problem.
• ✅ Verifying solutions involves substituting them back into the original equation and checking if they satisfy the equation.
• ❓ Absolute value equations can have multiple valid solutions, depending on the given absolute value.
• ❣️ A graphical interpretation of absolute value equations involves finding the x-values where the graph intersects the specified y-value line(s).
• 🌍 Understanding absolute value equations is crucial in solving various real-world problems.

Questions & Answers

Q: How do you solve absolute value equations?

To solve absolute value equations, set the expression inside the absolute value sign equal to both the positive and negative values of the given absolute value, and solve for the variable in each case.

Q: Why are there two possible solutions for absolute value equations?

Absolute value equations have two possible solutions because the absolute value of a number can be equal to either the positive or negative value of that number. This is due to the fact that the distance of any number from zero is the same irrespective of its sign.

Q: How do you verify the solutions to an absolute value equation?

To verify the solutions to an absolute value equation, substitute each solution back into the original equation and check if it satisfies the equation. If the expression inside the absolute value sign evaluates to the given absolute value, then the solution is correct.

Q: Can an absolute value equation have no solution?

Yes, an absolute value equation can have no solution. This occurs when there are no values for the variable that satisfy the equation after considering both the positive and negative values of the absolute value expression.

Summary & Key Takeaways

• Absolute value equations can be solved by considering both the positive and negative values of the absolute value expression.

• To solve the equation |2x - 5| = 11, set the expression inside the absolute value sign equal to both 11 and -11, and solve for x in each case.

• The solutions to the equation |2x - 5| = 11 are x = 8 and x = -3.