Answer
a. $|1-\sqrt 2|$ =$ -(1-\sqrt 2) $ = $\sqrt 2 - 1$
b. $|\pi-3|$ = $\pi-3$
c. $|x|/x$ = 1
Work Step by Step
a. The number inside the absolute value bars, $|1-\sqrt 2|$ , is
negative.
Because $\sqrt 2$ $\approx$ 1.414.$ (1-1.414) $ = -0.414.
The absolute value of negative number is negative. Thus $|1-\sqrt 2|$ =$ -(1-\sqrt 2) $
=$\sqrt 2 - 1$
b. The number inside the absolute value bars is positive. Because $\pi\approx3.14$. Thus |3.14 - 3| $\gt$ 0. The absolute value of a positive number is the number itself. So,
$|\pi-3|$ = $\pi-3$
c. If x$\gt$0, then $|x|$ = x. Thus, $|x|/x$ = $x/x$ = 1
