Question
From the definition of absolute value, \( 3|x|= \) Choose... when \( x \geq 0 \) and \( 3|x|= \) Choose... when \( x<0 \).
Ask by Barber Griffin. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
When \( x \geq 0 \), \( 3|x| = 3x \). When \( x < 0 \), \( 3|x| = -3x \).
Solution
- For \( x \geq 0 \):
Since by definition \( |x| = x \) when \( x \geq 0 \), we have
\[
3|x| = 3x.
\]
- For \( x < 0 \):
Since by definition \( |x| = -x \) when \( x < 0 \), we have
\[
3|x| = -3x.
\]
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Simplify this solution Extra Insights
When \( x \geq 0 \), we can simply drop the absolute value sign, giving us \( 3|x| = 3x \). Think of it like a superhero—it’s always positive when in the light! On the flip side, when \( x < 0 \), the absolute value flips the sign to make it positive, resulting in \( 3|x| = 3(-x) = -3x \). Here, the negative x becomes a heroic positive in disguise!
