Question:
If $|b| \geq |a|$ and $x = |a| - b$, then which one of the following is necessarily true?
If $|b| \geq |a|$ and $x = |a| - b$, then which one of the following is necessarily true?
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When solving absolute value inequalities, always consider the possible cases for both positive and negative values of the variables.
Updated On: Aug 1, 2025
- $a - x \leq 0$
- $a - x \geq 0$
- $a - x \geq b$
- $a - x \leq b$
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The Correct Option is D
Solution and Explanation
Given that $|b| \geq |a|$ and $x = |a| - b$, we can substitute into the expression $a - x$ to evaluate the inequality. Since $|b| \geq |a|$, it follows that $a - x \leq b$.
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