Chapter 1.9, Problem 33E

To determine

To calculate: The value of $x$ from the equation $\frac{2}{x}+\frac{1}{2x}=7$ by algebraic method and graphical method.

Answer to Problem 33E

The value of $x$ is $-6$ and Graph of the equation is provided below,

  

Explanation of Solution

Given information:

The equation $\frac{2}{x}+\frac{1}{2x}=7$ .

Calculation:

It is provided that the equation $\frac{2}{x}+\frac{1}{2x}=7$ .

Algebraic method;

The method in which isolate $x$ on one side of the equation and solve the value of $x$ .

Subtract $-2x$ from the equation $\frac{2}{x}+\frac{1}{2x}=7$ ,

  $\begin{array}{l}\frac{2}{x}+\frac{1}{2x}=7\\ \frac{5}{2x}=7\end{array}$

Solve the value of $x$ from the equation,

  $\begin{array}{l}\frac{5}{2x}=7\\ \frac{5}{14}=x\end{array}$

Therefore, the value of $x=\frac{5}{14}$ .

Graphical method;

Let put $y_1=7$ and $y_2=\frac{2}{x}+\frac{1}{2x}$

The graph of the equation $y_1=7$ provided below,

  

The graph of the equation $y_2=\frac{2}{x}+\frac{1}{2x}$ can be sketched using the table,

$x$	$y_2$
1	$\frac{5}{2}$
2	$\frac{5}{4}$
4	$\frac{5}{8}$
$-2$	$-\frac{5}{4}$
$-4$	$-\frac{5}{8}$

The graph of equation is provided below,

  

The graph of both equations in same figure is provided below,

  

The solution is the $x$ coordinate of the intersection point $\left(\frac{5}{14},7\right)$ of the two graphs. So, the intersection point on the $x$ coordinate is $\frac{5}{14}$ .

Thus, the value of $x$ is $\frac{5}{14}$ .