Understanding Absolute Value Equations

The video tutorial explains how to solve absolute value equations by breaking them into two separate linear equations. It provides two examples: solving |3x + 2| = 8 and |7 - 2x| = 10. The process involves removing the absolute value bars and solving the resulting equations for both positive and negative scenarios. The tutorial emphasizes checking solutions by substituting them back into the original equation.

What must be true about the value of B in an absolute value equation |A| = B for it to have solutions?

• B can be any real number

• B must be greater than or equal to 0

• B must be greater than 0

• B must be less than 0

When solving an absolute value equation, what are the two equations you need to solve?

• A = B and A = B^2

• A = B and A = 1

• A = B and A = -B

• A = B and A = 0

In the equation |3x + 2| = 8, what is the first step to find the solutions?

• Divide both sides by 3

• Multiply both sides by 3

• Subtract 2 from both sides

• Add 2 to both sides

What is one of the solutions for the equation |3x + 2| = 8?

• x = 3

• x = 2

• x = -2

• x = 0

What is the second solution for the equation |3x + 2| = 8?

• x = 3

• x = -3

• x = 10/3

• x = -10/3

In the equation |7 - 2x| = 10, what is the first step to solve for x?

• Divide both sides by 2

• Multiply both sides by 2

• Add 7 to both sides

• Subtract 7 from both sides

What is one of the solutions for the equation |7 - 2x| = 10?

• x = -5

• x = 5

• x = -3/2

• x = 3/2

What is the second solution for the equation |7 - 2x| = 10?

• x = 17/2

• x = -17/2

• x = -7

• x = 7

Why is it important to check the solutions of an absolute value equation?

• To find additional solutions

• To verify the arithmetic and confirm the solutions satisfy the original equation

• To simplify the solutions

• To ensure the solutions are positive

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

• Add them together

• Multiply them by 2

• Check them by substituting back into the original equation

• Ignore them