Chapter 1.4, Problem 60E

(a)

To determine

To find:the minimum and maximum percent of voters who could vote republican.

Answer to Problem 60E

  $\begin{array}{l}42-2=40.\\ 42+2=44.\end{array}$

Explanation of Solution

Given:

  

Concept used:

Absolute value or modulus of a real number $x$ ,denoted that $\left|x\right|$ , is the non-negative value of $x$ without regard to its sign.

Mathematically,

  $\left|x\right|=x.$

If domain $x$ is positive.

  $\left|x\right|=-x.$

If domain $x$ is negative.

Calculation:

First compute the minimum and maximum percent of voter for the republicans:

  $\begin{array}{l}42-2=40.\\ 42+2=44.\end{array}$

Compute the minimum and maximum percent of voters for the democrats:

  $\begin{array}{l}47-2=45.\\ 47+2=49.\end{array}$

Hence, $42-2=40,42+2=44.$

(b)

To determine

To find:the procedure to use absolute value equations to represent the answers in part a.

Answer to Problem 60E

  $\left|x-42\right|=2,\left|x-47\right|=2$ .

Explanation of Solution

Given:

  

Concept used:

Absolute value or modulus of a real number $x$ ,denoted that $\left|x\right|$ , is the non-negative value of $x$ without regard to its sign.

Mathematically,

  $\left|x\right|=x.$

If domain $x$ is positive.

  $\left|x\right|=-x.$

If domain $x$ is negative.

Calculation:

It can use the absolute value equations:

Republican:

  $\left|x-42\right|=2.$

Democrats:

  $\left|x-47\right|=2$.

Hence, $\left|x-42\right|=2,\left|x-47\right|=2$ .

(c)

To determine

To find:the one candidate received $44\%$ of the vote and party that belongs.

Answer to Problem 60E

The candidate belongs to the democrat party.

Explanation of Solution

Given:

  

Concept used:

Absolute value or modulus of a real number $x$ ,denoted that $\left|x\right|$ , is the non-negative value of $x$ without regard to its sign.

Mathematically,

  $\left|x\right|=x.$

If domain $x$ is positive.

  $\left|x\right|=-x.$

If domain $x$ is negative.

Calculation:

  $44\in \left[40,44\right]$ .

The candidate belongs to therepublican party.

  $44\in \left[42,49\right]$ .

Hence, the candidate belongs to the democrat party.