Easiest Way To Solve an Absolute Value Equation and Determine when Only One Solution

The video tutorial explains how to solve absolute value inequalities by setting up two cases: one positive and one negative. It emphasizes the importance of isolating the absolute value and solving for X by ensuring variables are on the same side. The tutorial also highlights the necessity of checking solutions, especially when dealing with variables on both sides, to ensure they are valid. The only valid solution in the example is X = 11/8, as absolute values cannot equal negative numbers.

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

• Distribute the negative sign

• Check the solutions

• Isolate the absolute value

• Set up two cases

Why do we set up two cases when solving absolute value inequalities?

• To simplify the equation

• To consider both positive and negative scenarios

• To avoid negative numbers

• To eliminate variables

What should you do after setting up the two cases in an absolute value inequality?

• Multiply by a constant

• Solve for X

• Check for extraneous solutions

• Add variables to both sides

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

• To confirm the solution satisfies the original equation

• To eliminate negative values

• To ensure the solution is positive

• To simplify the equation further

What happens if an absolute value equation results in a negative number?

• The equation needs to be simplified

• The equation has no solution

• The solution is extraneous

• The solution is valid