Simplify the expression for the given values of \( x \). \( |x|+|x-5| \) if \( 2 \leq x \leq 3 \) 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: \[ \boxed{5}. \]