Write the function f(x) = |x| + |x − 5| without using absolute value signs.

Possible answer:     =====definition of absolute value in terms of a piecewise expression    there are two different absolute value parts in the equation for function f.since x - 5  ≥ 0 has solution set x  ≥ 5 and x - 5 < 0 has solution set x < 0,for x  ≥ 5,  |x − 5| = x - 5 because the inside will be positive.for x < 5, |x - 5| = -(x-5) because the inside will be negative; that negative coefficient over the parentheses will turn the negatives into positive.for  x  ≥ 0,  |x| = xfor  x < 0, |x| = -xtherefore, we can create a piecewise definition broken apart into three intervals:     x ≤ 0, where |x| = -x and |x-5| = -(x-5)    0  < x  < 5, where |x| = x and |x-5| = -(x-5)    x ≥ 5, where |x| = x and |x-5| = x-5a possible function rule is    which can be simplified if we distribute negatives and combine like terms