How To Solve an Absolute Value Equation and Test Our Solutions when They Do Not Work

The video tutorial explains how to solve absolute value equations by setting up two cases: one where the absolute value is positive and another where it is negative. The process involves isolating the absolute value, creating cases, solving them, and testing the solutions. The tutorial concludes by explaining that if the solutions result in a negative value for an absolute value equation, there is no solution.

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

• Add a constant to both sides

• Subtract a variable from both sides

• Isolate the absolute value

• Multiply both sides by a variable

When setting up two cases for an absolute value equation, what should you consider?

• The variable being zero

• The expression inside the absolute value being both positive and negative

• The variable being negative

• The expression inside the absolute value being zero

In solving the equation 6 - 5X = 3X - 7, what is the result of adding 3X to both sides?

• 6 - 2X = 7

• 6 + 2X = 7

• 6 - 8X = 7

• 6 + 8X = 7

Why is it important to verify solutions in absolute value equations?

• To find additional solutions

• To simplify the equation further

• To confirm the solutions satisfy the original equation

• To ensure the solutions are positive

What conclusion can be drawn if the solutions to an absolute value equation do not satisfy the original equation?

• The solutions are incorrect

• The equation needs to be simplified further

• There is no solution

• There are multiple solutions