Chapter 3.1, Problem 1MRE

To determine

To evaluate: the given expression.

Answer to Problem 1MRE

  $a-\left|c-b\right|=3$

Explanation of Solution

Given information:

Given expression

  $a-\left|c-b\right|$

And

  $a=4,b=-6,c=-7$ , and $d=5$ .

Concept used:

Absolute value of a function a is given by

  $\left|a\right|=\{\begin{array}{l}aa>0\\ -aa<0\\ 0a=0\end{array}$ \

And

  $\begin{array}{l}\left|-a\right|=a\\ \left|a\right|=a\end{array}$

Calculation:

Consider the given expression.

  $a-\left|c-b\right|$

Substitute the value of $a,b$ , and $c$ in the given expression,

  $\begin{array}{c}a-\left|c-b\right|=4-\left|-7-\left(-6\right)\right|\\ =4-\left|-7+6\right|\\ =4-\left|-1\right|\\ =4-1\left[\left|-a\right|=a\right]\\ =3\end{array}$

Hence, the value of the expressionis $3$ .