Chapter 1.1, Problem 48E

To determine

To fill the given table

Answer to Problem 48E

Equation	Value of x
$x-c=0$	Increases
$cx=1$	Decreases
$cx=c$	Stay the same
$\frac{x}{c}=1$	Increases

Explanation of Solution

Given:

  

Calculation:

Consider the first equation,

  $x-c=0$

  $\Rightarrow x=c$

When c increases, then x obviously increases.

Consider the second equation,

  $cx=1$

  $\Rightarrow x=\frac{1}{c}$

Here, x and c are inversely proportional.

Thus, as c increases, x decreases

Consider the third equation,

  $cx=c$

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

Here, the value of x stays the same for all values of c.

Consider the last equation,

  $\frac{x}{c}=1$

  $\Rightarrow x=c$

Thus, as c increases, x also increases.

Conclusion:

Therefore, the table becomes as

Equation	Value of x
$x-c=0$	Increases
$cx=1$	Decreases
$cx=c$	Stay the same
$\frac{x}{c}=1$	Increases