Solving Absolute Value Equations

This video tutorial continues the exploration of solving absolute value equations, focusing on equations with variables on both sides. It begins with a review of the algebraic definition of absolute value, explaining how it applies to positive, zero, and negative numbers. The tutorial then introduces a method for solving these equations by considering two cases: when the quantity inside the absolute value is positive and when it is negative. The concept of extraneous solutions is explained, highlighting the importance of verifying solutions. Two example problems are solved step-by-step, illustrating the process and the identification of extraneous solutions.

What is the main focus of this video tutorial?

• Solving quadratic equations

• Graphing linear equations

• Solving absolute value equations with variables on both sides

• Solving linear equations

What does the algebraic definition of absolute value depend on?

• The type of equation

• The size of the number

• Whether the number is positive, zero, or negative

• Whether the number is even or odd

If the absolute value of a positive number is taken, what is the result?

• Zero

• The opposite of the number

• The number itself

• A negative number

When solving absolute value equations with variables on both sides, how many cases must be considered?

• One

• Four

• Two

• Three

What is an extraneous solution?

• A solution that is always correct

• A solution that satisfies the original equation

• A solution that is always incorrect

• A solution that does not satisfy the original equation

In the first example problem, what is the first step in solving the equation?

• Add variables to both sides

• Subtract variables from both sides

• Assume the quantity inside the absolute value is positive

• Assume the quantity inside the absolute value is negative

How do you verify if a solution is extraneous?

• By checking if it is a positive number

• By checking if it satisfies the original equation

• By checking if it is a negative number

• By checking if it satisfies a modified equation

In the second example problem, what is assumed about the quantity 4 + 3x?

• It is always zero

• It is a positive quantity

• It is a negative quantity

• It is an extraneous solution

What should be done after finding apparent solutions to an equation?

• Use them in another equation

• Assume they are correct

• Ignore them

• Verify them by substituting back into the original equation