Chapter 1.1, Problem 48E

(a)

To determine

To indicate the value of $x$ when value of $c$ increases for the below equation and $c$ is a positive constant −

  $x-c=0$

Answer to Problem 48E

  $x$ increases when value of $c$ increases.

Explanation of Solution

Given:

Equation: $x-c=0$ ; $c$ is a positive constant

Calculation:

Given:

Equation: $x-c=0$ ; $c$ is a positive constant

Solving the above equation, we have:

  $\begin{array}{l}x-c=0\\ x=c\end{array}$

Since, $x=c$ , so if value of $c$ increases, then the value of $x$ will increase

Conclusion:

Hence, $x$ increases when value of $c$ increases.

(b)

To determine

To indicate the value of $x$ when value of $c$ increases for the below equation and $c$ is a positive constant −

  $cx=1$

Answer to Problem 48E

  $x$ decreases when value of $c$ increases.

Explanation of Solution

Given:

Equation: $cx=1$ ; $c$ is a positive constant

Calculation:

Given:

Equation: $cx=1$ ; $c$ is a positive constant

Solving the above equation, we have:

  $\begin{array}{l}cx=1\\ x=\frac{1}{c}\end{array}$

Since, $x=\frac{1}{c}$ , so if value of $c$ increases, then the value of $x$ will decrease

Conclusion:

Hence, $x$ decreases when value of $c$ increases.

(c)

To determine

To indicate the value of $x$ when value of $c$ increases for the below equation and $c$ is a positive constant −

  $cx=c$

Answer to Problem 48E

  $x$ stays the same even when value of $c$ increases.

Explanation of Solution

Given:

Equation: $cx=c$ ; $c$ is a positive constant

Calculation:

Given:

Equation: $cx=c$ ; $c$ is a positive constant

Solving the above equation, we have:

  $\begin{array}{l}cx=c\\ x=\frac{c}{c}\\ x=1\end{array}$

Since, $x=1$ , so even if value of $c$ increases, then the value of $x$ will remain as $1$ .

Conclusion:

Hence, $x$ stays the same even when value of $c$ increases.

(d)

To determine

To indicate the value of $x$ when value of $c$ increases for the below equation and $c$ is a positive constant −

  $\frac{x}{c}=1$

Answer to Problem 48E

  $x$ increases when value of $c$ increases.

Explanation of Solution

Given:

Equation: $\frac{x}{c}=1$ ; $c$ is a positive constant

Calculation:

Given:

Equation: $\frac{x}{c}=1$ ; $c$ is a positive constant

Solving the above equation, we have:

  $\begin{array}{l}\frac{x}{c}=1\\ x=c\end{array}$

Since, $x=c$ , so if value of $c$ increases, then the value of $x$ increases.

Conclusion:

Hence, $x$ increases when value of $c$ increases.