Exercise · ZW-ABSOLUTE-VALUE-REAL-007 · ★★☆ Intermediate
If \(|x|=3\) and \(|y|=4\), what is the largest possible value of \(|x+y|\)?
Choose one option.
Show answer
- D. \(7\)
Explanation
By the triangle inequality \(|x+y|\le|x|+|y|=7\), attained at \(x=3,\ y=4\).
Review the concept: Absolute value
The absolute value \(|x|\) of a real number \(x\) is its distance from zero on the real line; \(|x-a|\) measures the distance between \(x\) and \(a\).
\[|x|=\begin{cases}x,&x\ge0\\-x,&x<0\end{cases}\]
More practice problems: absolute value
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- ZW-ABSOLUTE-VALUE-REAL-004 The inequality |x-4|<2 is equivalent to:
- ZW-ABSOLUTE-VALUE-REAL-005 Which equality holds for all reals x,y?
- ZW-ABSOLUTE-VALUE-REAL-006 Solve |2x-1|≤5.
- ZW-ABSOLUTE-VALUE-REAL-008 If |x|=5 and |y|=2, what is the smallest possible value of |x-y|?
- ZW-ABSOLUTE-VALUE-REAL-009 If |x|<ε for every ε>0, then: