Pregunta
Simplify the expression for the given values of \( x \). \( |x|+|x-5| \) if \( 2 \leq x \leq 3 \) Answer:
Ask by Colon Coleman. in the United States
Mar 13,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The simplified expression is 5.
Solución
For \( 2 \leq x \leq 3 \):
1. Since \( x \geq 2 > 0 \), we have
\[
|x| = x.
\]
2. For \( |x-5| \), note that
\[
x-5 \leq 3-5 = -2,
\]
so \( x-5 \) is negative in this interval, and therefore,
\[
|x-5| = -(x-5) = 5-x.
\]
3. Substitute the expressions:
\[
|x| + |x-5| = x + (5-x) = 5.
\]
The simplified expression is \(\boxed{5}\).
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Como
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Beyond the Answer
To simplify \( |x| + |x-5| \) for the given range \( 2 \leq x \leq 3 \), we first analyze the expressions inside the absolute value signs. For \( x \) in the range \( 2 \leq x \leq 3 \): - \( |x| = x \) because \( x \) is positive. - \( |x-5| = 5 - x \) because \( x - 5 \) is negative (for values less than 5). Now we substitute these into the original expression: \[ |x| + |x-5| = x + (5 - x) = 5. \] Thus, the simplified expression for \( |x| + |x-5| \) when \( 2 \leq x \leq 3 \) is: \[ \boxed{5}. \]

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