Chapter 1.2, Problem 55E

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 55E

  $x=-\frac{8}{b}$ .

Explanation of Solution

Given:

  $2bx-bx=-8$ .

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 $b\ne 0$ .

Probably the most common thing it will be doing with polynomials is combining like terms.

This is the process of adding together whatever terms it can, but not overdoing it by trying to add together terms that can’t actually be combined and term can combineonly if there has the exact same variable portion and exact same variable portion and by exact same.

Calculation:

According to the given:

  $2bx-bx=-8$ .

Combining the like term as:

  $bx=-8.$

Dividing both the side by $b$ :

  $x=-\frac{8}{b}$ .

Here variable $b$ 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, $x=-\frac{8}{b}$ .