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Questions and Answers
What is the first step in solving the absolute value equation |3x + 5| - 7 = 10?
What is the first step in solving the absolute value equation |3x + 5| - 7 = 10?
How many solutions does the absolute value equation |5x - 2| = 0 have?
How many solutions does the absolute value equation |5x - 2| = 0 have?
Solve for x in the absolute value equation: |x - 4| = 7
Solve for x in the absolute value equation: |x - 4| = 7
Which of the following is a valid algebraic manipulation when solving for x in the equation |2x + 1| - 5 = 4?
Which of the following is a valid algebraic manipulation when solving for x in the equation |2x + 1| - 5 = 4?
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Study Notes
Solving Absolute Value Equations
- When solving absolute value equations, there are possibilities of 1, 2, or no solutions.
Solving Process
- Isolate the absolute value bars: Get the absolute value expression by itself on one side of the equation.
- Remove the absolute value bars and split the equation: Create two separate equations. One equation will keep the expression inside the absolute value bars the same, and the other will change the expression to its opposite.
- Solve for x: Solve each equation independently to find the solutions for x.
Example
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Original Equation: |2x - 3| - 20 = -15
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Isolate absolute value bars: Add 20 to both sides to get |2x - 3| = 5
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Create two equations:
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2x - 3 = 5
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2x - 3 = -5
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Solve first equation:
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2x = 8
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x = 4
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Solve second equation:
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2x = -2
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x = -1
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Solutions: x = 4, x = -1
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Description
This quiz focuses on the method of solving absolute value equations, where solutions may vary. You'll learn how to isolate the absolute value, split the equation, and solve for the unknown variable. Test your understanding with examples provided to reinforce the concept.
