Math Problem Statement
Solution
Let's solve each of the given equations one by one.
(a)
For an absolute value equation like , we have two cases to solve:
So, the solution set for part (a) is and .
(b)
The absolute value of any expression is zero only if the expression itself is zero. Therefore:
So, the solution set for part (b) is .
(c)
An absolute value cannot be negative, so there are no solutions for this equation.
Summary of Solutions:
- (a)
- (b)
- (c) No solution
Would you like further details on any step? Here are five related questions to expand on this:
- What are the properties of absolute value equations?
- How can absolute value inequalities be solved?
- Can absolute value equations have no solutions, and why?
- How do you graph absolute value functions?
- What is the geometric interpretation of an absolute value equation?
Tip: When solving absolute value equations, always remember to check for both the positive and negative cases!
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Math Problem Analysis
Mathematical Concepts
Absolute Value
Linear Equations
Formulas
|x| = y implies x = y or x = -y
Theorems
The definition of absolute value
No solution for negative absolute values
Suitable Grade Level
Grades 6-8