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Questions and Answers
What is the first step in solving an absolute value equation?
What is the first step in solving an absolute value equation?
- Divide both sides by a constant
- Add or subtract a constant from both sides (correct)
- Solve for the variable
- Apply the absolute value rule
What is the result of the equation $5|4x-3| = 20$ after isolating the absolute value?
What is the result of the equation $5|4x-3| = 20$ after isolating the absolute value?
- $|4x-3| = 4$ (correct)
- $|4x-3| = 2$
- $|4x-3| = 20$
- $|4x-3| = 5$
What are the two cases we solve for after applying the absolute value rule to $|4x-3| = 4$?
What are the two cases we solve for after applying the absolute value rule to $|4x-3| = 4$?
- $4x+3 = 4$ or $4x+3 = -4$
- $4x-3 = 4$ or $4x-3 = -4$ (correct)
- $4x+3 = 4$ or $4x-3 = -4$
- $4x-3 = 4$ or $4x+3 = -4$
What are the solutions to the equations $4x-3 = 4$ and $4x-3 = -4$?
What are the solutions to the equations $4x-3 = 4$ and $4x-3 = -4$?
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What is the purpose of checking for extraneous solutions when solving an absolute value equation?
What is the purpose of checking for extraneous solutions when solving an absolute value equation?
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Study Notes
Solving Absolute Value Equations: The First Step
- Isolate the absolute value expression. This means getting the expression containing the absolute value symbol by itself on one side of the equation.
Isolating the Absolute Value
- For the equation 5|4x - 3| = 20, isolating the absolute value results in |4x - 3| = 4.
Applying the Absolute Value Rule
- After isolating the absolute value, we solve two separate equations:
- Case 1: 4x - 3 = 4
- Case 2: 4x - 3 = -4
Solving the Equations
- The solution to 4x - 3 = 4 is x = 7/4.
- The solution to 4x - 3 = -4 is x = -1/4.
Checking for Extraneous Solutions
- Checking for extraneous solutions is crucial because operations performed during the solving process might introduce solutions that don't satisfy the original equation. Extraneous solutions must be rejected.
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