Solving Absolute Value Equations with Variables on Both Sides

What is the first step to take when solving an absolute value equation?

• Isolate the variable

• Distribute the negative sign

• Combine like terms

• Isolate the absolute value

When creating the first case for an absolute value equation, what should you do?

• Rewrite the equation without absolute value

• Add the absolute value to both sides

• Square both sides

• Multiply both sides by -1

What common mistake do students make when negating the second case?

• Forgetting to isolate the absolute value

• Not using parentheses

• Multiplying instead of dividing

• Adding instead of subtracting

How should you handle the negative sign when creating the second case?

• Ignore it

• Apply it to the constant term

• Only apply it to the variable

• Apply it to the entire side using parentheses

What is the goal when solving for the variable in an absolute value equation?

• Make the variable negative

• Isolate the constant term

• Make the variable positive

• Combine like terms

If you prefer the variable on a specific side, what can you do after solving?

• Leave it as is

• Switch it to the other side

• Multiply both sides by -1

• Add the variable to both sides

Why is it important to check for extraneous solutions?

• To isolate the variable

• To ensure the solution is positive

• To verify the solution satisfies the original equation

• To simplify the equation

What should you do if the absolute value equals a negative number?

• Ignore it

• Consider it a valid solution

• Label it as extraneous

• Multiply by -1

What is the result when plugging in -3 into the equation 4 * -3 + 5?

• -7

• -1

• 7

• 1

What is the final step after solving the absolute value equation?

• Distribute the negative sign

• Isolate the variable

• Check for extraneous solutions

• Combine like terms