Chapter 1.2, Problem 54E

To determine

Tofind:the solution of the equation for $x$ if the letter a, b and c are represented non zero constants.

Answer to Problem 54E

  $x=\frac{c-b}{a}$ .

Explanation of Solution

Given:

  $ax+b=c$ .

Concept used:

The ratio of two numbers $a\text{ and }b$ .

  $\begin{array}{l}r=\frac{a}{b}.\\ a=r\times b.\end{array}$

Well if $b=0$ such that, it is trying to divide by zero it has to find the number $r$ such that:

  $\begin{array}{l}r\times 0=a\left(1\right).\\ r\times 0=0.\end{array}$

If $b=0.$ then the $r=\infty$ . Which it exact does not exist.

For a rational number $b\ne 0$ .

Calculation:

According to the given:

  $ax+b=c$ .

Subtracting both the side by $b$ :

  $\begin{array}{l}ax+b-b=c-b.\\ \Rightarrow ax=c-b.\end{array}$

Dividing both the side by $a$ :

  $x=\frac{c-b}{a}$ .

Here variable $a$ should not be zero if it is zero the value of $x$ doesn’t exist therefore, $b\ne 0$ to have the value rational.

Hence, $x=\frac{c-b}{a}$ .