Chapter 1.1, Problem 1E

(a)

To determine

The expression without using the absolute value symbol

Answer to Problem 1E

  $\left(-5\right)\cdot 3$

Explanation of Solution

Given:

The given expression is

  $\left(-5\right)\left|3-6\right|$

Calculation:

The absolute value $\left|a\right|$ of a real number ‘a’ can be defined as

  $\left|a\right|=\{\begin{array}{l}aifa\ge 0\\ -aifa\ge 0\end{array}$

Therefore, the absolute value of the given expression will be

  $\begin{array}{c}\left(-5\right)\left|3-6\right|=\left(-5\right)\left|-3\right|\\ =\left(-5\right)\left[-\left(-3\right)\right]\\ =\left(-5\right)\cdot 3\end{array}$

(b)

To determine

The expression without using the absolute value symbol

Answer to Problem 1E

  $6/\left(-2\right)$

Explanation of Solution

Given:

The given expression is

  $\left|-6\right|/\left(-2\right)$

Calculation:

The absolute value $\left|a\right|$ of a real number ‘a’ can be defined as

  $\left|a\right|=\{\begin{array}{l}aifa\ge 0\\ -aifa\ge 0\end{array}$

Therefore, the absolute value of the given expression will be

  $\begin{array}{c}\left|-6\right|/\left(-2\right)=\frac{\left|-6\right|}{\left(-2\right)}\\ =\frac{-\left(-6\right)}{-2}\\ =\frac{6}{-2}\\ =6/\left(-2\right)\end{array}$

(c)

To determine

The expression without using the absolute value symbol

Answer to Problem 1E

  $7+4$

Explanation of Solution

Given:

The given expression is

  $\left|-7\right|+\left|4\right|$

Calculation:

The absolute value $\left|a\right|$ of a real number ‘a’ can be defined as

  $\left|a\right|=\{\begin{array}{l}aifa\ge 0\\ -aifa\ge 0\end{array}$

Therefore, the absolute value of the given expression will be

  $\begin{array}{c}\left|-7\right|+\left|4\right|=-\left(-7\right)+4\\ =7+4\end{array}$