뒤로College Algebra Study Guide: Absolute Value Equations
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Q1. Solve the absolute value equation or indicate that the equation has no solution.
Background
Topic: Absolute Value Equations
This question is testing your understanding of how to solve equations involving absolute values, and how to determine if an equation has no solution.
Key Terms and Formulas
Absolute value: represents the distance of from zero on the number line, always non-negative.
General approach: To solve , consider two cases:
If , then has no solution, since absolute value cannot be negative.
Step-by-Step Guidance
Identify the absolute value equation you need to solve. For example, .
Check if the right side () is negative. If it is, the equation has no solution.
If is non-negative, set up two cases:
Case 1:
Case 2:
Solve each case for and write the solution set. If the equation is more complex (e.g., ), set and and solve each.
Check your solutions in the original equation to ensure they are valid.
Try solving on your own before revealing the answer!
Final Answer:
The solution set depends on the specific equation. If the right side is negative, the solution set is the empty set (). If the right side is non-negative, the solution set is the two values found by solving both cases.
For example, for , the solution set is and .
If the equation is , the solution set is the empty set because absolute value cannot be negative.
