If x > 10 or x < -10, then which of the following is true regarding |x|?
Understand the Problem
The question is asking about the implications of the conditions on x in terms of absolute value expressions. We need to determine the correct relationship involving |x| that follows from the given conditions.
Answer
The answer is $|x| > 10$.
Answer for screen readers
The correct relationship is $|x| > 10$.
Steps to Solve
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Understanding the absolute value expression The statement given is "if $x > 10$ or $x < -10$". This indicates that $x$ is either greater than 10 or less than -10.
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Analyzing the implications of $x > 10$ If $x > 10$, then the absolute value $|x|$ must also be greater than 10 since absolute value represents the distance of $x$ from 0 regardless of direction. Thus, for $x > 10$, we can conclude: $$ |x| > 10 $$
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Analyzing the implications of $x < -10$ Similarly, if $x < -10$, the absolute value $|x|$ must also be greater than 10, because distances are always positive. Hence, if $x < -10$, we again conclude: $$ |x| > 10 $$
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Combining the results Since both scenarios ($x > 10$ or $x < -10$) lead to the same conclusion, we can combine these reasoning steps: If either condition is true, then it follows that: $$ |x| > 10 $$
The correct relationship is $|x| > 10$.
More Information
This conclusion is derived from the properties of absolute values. Absolute value measures the distance from zero on a number line, so any value of $x$ that is greater than 10 or less than -10 will have an absolute value greater than 10.
Tips
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