Algebra 2 - 1C - Absolute Value Equations

What is the first step in solving absolute value equations?

What is the second step in solving absolute value equations?

What is the third step of solving absolute value equations?

What is the fourth step in solving absolute value equations?

What is the solution set for |x|=2?

What is the solution set for |5z|=40?

What is the solution set for |d+1|=8?

What is the solution set for |c|+2=12?

What is the solution set for 6|x|=24?

Steps to Solve Absolute Value Equations

Isolate the Absolute Value Expression: Ensure the absolute value expression is alone on one side of the equation before proceeding.
Set Up Two Equations: Equate the expression inside the absolute value to both the positive and negative values of the other side of the equation.
Solve Both Equations: Carefully solve each equation obtained from the previous step to find all possible solutions.
Express as a Solution Set: Present the final answers in the format ( x = { _, _ } ) for clarity.

Example Solutions

For |x| = 2: The solution set is ( x = {-2, 2} ).
For |5z| = 40: The solution set is ( z = {8, -8} ).
For |d + 1| = 8: The solution set is ( d = {7, -9} ).
For |c| + 2 = 12: After solving, the solution set is ( c = {10, -10} ).
For 6|x| = 24: The solution set is ( x = {4, -4} ).

Key Concepts

Absolute value equations can yield multiple solutions due to their definition involving both positive and negative outcomes.
Always check solutions in the original equation to ensure they are valid, especially in complex cases.

Test your knowledge on solving absolute value equations with this flashcard quiz. Learn the steps required to isolate the absolute value expression and find the solutions. Perfect for mastering algebraic concepts in your Algebra 2 course!