Math Problem Statement
solve
Solution
To solve the equation:
We need to consider two cases because of the absolute value:
Case 1:
In this case, we can remove the absolute value and solve for :
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Add to both sides to get rid of the on the right-hand side:
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Add 4 to both sides to isolate the term with :
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Divide both sides by 4 to solve for :
Case 2:
In this case, remove the absolute value by setting the expression equal to the negative of the right-hand side:
Simplify the right-hand side:
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Subtract from both sides:
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Add 4 to both sides:
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Divide both sides by 2 to solve for :
Verifying solutions:
For :
For :
Final Solutions:
Let me know if you would like more details or if you have any questions.
Here are 5 related questions for practice:
- Solve .
- Solve .
- Solve .
- Solve .
- Solve .
Tip: When solving absolute value equations, always split the equation into two cases: one for the positive expression and one for the negative expression.
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Math Problem Analysis
Mathematical Concepts
Algebra
Absolute Value Equations
Formulas
|A| = B → A = B or A = -B
Theorems
Absolute Value Property
Suitable Grade Level
Grades 8-10