Chapter 2.3, Problem 64E

To determine

To select: the correct value of x from the given option.

Answer to Problem 64E

A. $-3$

Explanation of Solution

Given information:

The given equation is as follows:

  $\frac{2x-3}{x}=\frac{3-x}{2}$

The options are as follows:

  $\begin{array}{l}\text{A }-3\\ \text{B }-1\\ \text{C 37}\\ \text{D 5}\\ \text{E 15}\end{array}$

Calculation:

Solve the equation as follows:

  $\begin{array}{c}\frac{2x-3}{x}=\frac{3-x}{2}\\ 2\left(2x-3\right)=x\left(3-x\right)\left[\text{Taking Common factor}\right]\\ 4x-6=3x-x^2\left[\text{Distribute}\right]\\ x^2+x-6=0\\ \left(x+3\right)\left(x-2\right)=0\left[\text{Factor}\right]\end{array}$

  $\therefore x=-3\text{ or }2$

According to the option, the value of x should be $-3$ . Thus, option A is correct.