Algebra 2 - 1C - Absolute Value Equations

Questions and Answers

What is the first step in solving absolute value equations?

Make sure the absolute value expression is isolated.

What is the second step in solving absolute value equations?

Set the 'inside' equal to both the positive and negative number from the other side of the equation.

What is the third step of solving absolute value equations?

Solve both equations.

What is the fourth step in solving absolute value equations?

Write your answer as solution set x={,} Signup and view all the answers

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

x={-2,2} Signup and view all the answers

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

z={8,-8} Signup and view all the answers

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

d={7,-9} Signup and view all the answers

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

c={10,-10} Signup and view all the answers

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

x={4,-4} Signup and view all the answers

Study Notes

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.

Description

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!