Algebra II Recipe: Solving Absolute Value Equations and Inequalities

1. Isolate the absolute value.
2. Write a compound sentence with "OR" between the two sentences.
   • Sentence 1 - is the expression inside the absolute value symbol set equal to the positive value of the right side of the equation.
   • Sentence 2 - is the expression inside the absolute value symbol set equal to the negative value of the right side of the equation.
3. Solve each sentence or equation.
4. Check each solution where the absolute value is isolated.
5. The answer is No Solution if neither number produces a true statement when checked.

1. Isolate the absolute value.
2. Write the compound sentence.
   • With "and" if you have < or ≤ after isolating.
   • With "or" if you have > or ≥ after isolating.
   • Sentence 1 is the isolated inequality without the absolute value symbols.
   • Sentence 2 looks like sentence 1, EXCEPT, change (flip) the inequality symbol and change the value on the right to its opposite.
3. Solve each sentence or inequality.
4. Graph the solution.