Solving Absolute value equations with a variable on both sides

The video tutorial explains how to handle absolute value equations by isolating the absolute value and creating two cases. It emphasizes the importance of using parentheses when negating expressions to avoid common mistakes. The tutorial provides step-by-step guidance on solving equations, ensuring the variable remains positive, and checking solutions to identify extraneous results. The instructor encourages students to practice with provided problems and collaborate for better understanding.

What is the first step in solving an equation with an absolute value?

• Add a constant to both sides

• Multiply both sides by a variable

• Isolate the absolute value

• Divide both sides by a constant

When creating the second case for an absolute value equation, what must you remember to do?

• Add parentheses around the expression

• Leave the expression unchanged

• Negate the entire expression inside the absolute value

• Multiply the expression by zero

Why might you choose to switch the side of the variable when solving an equation?

• To avoid using parentheses

• To make the variable negative

• To simplify the equation

• To ensure the variable remains positive

What should you do after finding potential solutions to an absolute value equation?

• Add them together

• Multiply them by a constant

• Verify by plugging them back into the original equation

• Ignore them and move on

What is an extraneous solution?

• A solution that satisfies the equation

• A solution that does not satisfy the original equation

• A solution that is always positive

• A solution that is always negative