QQuestionMathematics
QuestionMathematics
Solve the following absolute value equation.
What is the solution to the absolute value equation ∣x∣= 7?
A. x= 7
B. x=−7
C. x= 7 or x=−7
D. No solution
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Answer
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Step 1:I'll solve this absolute value equation step by step:
Step 2:: Understand the Absolute Value Equation
The equation $$|x| = 7$$ means we're looking for all values of x that, when their absolute value is taken, equal 7.
Step 3:: Solve the Positive Case
When $$|x| = 7$$, this means x could be a positive or negative number that is 7 units away from zero.
Step 4:: List the Possible Solutions
- Negative case: $$x = -7
The two solutions are:
Step 5:: Verify the Solutions
- For $$x = 7$$: $$|7| = 7$$ ✓
- For x = - 7: |- 7| = 7 ✓
Final Answer
x = - 7, which corresponds to option C. The correct answer is C. x = 7 or x = −7.
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