Chapter 1.9, Problem 32E

To determine

To calculate: The value of $x$ from the equation $\frac{1}{2}x-3=6+2x$ by algebraic method and graphical method.

Answer to Problem 32E

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

  

Explanation of Solution

Given information:

The equation $\frac{1}{2}x-3=6+2x$ .

Calculation:

It is provided that the equation $\frac{1}{2}x-3=6+2x$ .

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 $\frac{1}{2}x-3=6+2x$ ,

  $\begin{array}{c}\frac{1}{2}x-2x-3=6+2x-2x\\ \frac{3}{2}x-3=6\end{array}$

Add 3 in the equation,

  $\begin{array}{c}\frac{3}{2}x-3+3=6+3\\ \frac{3}{2}x=9\\ x=6\end{array}$

Therefore, the value of $x=6$ .

Graphical method;

Let put $y_1=\frac{1}{2}x-3$ and $y_2=6+2x$

The graph of the equation $y_1=\frac{1}{2}x-3$ can be sketched using the table,

$x$	$y_1$
0	$-3$
2	$-2$
4	$-1$
$-2$	$-4$
$-4$	$-5$

The graph of equation is provided below,

  

The graph of the equation $y_2=6+2x$ can be sketched using the table,

$x$	$y_2$
0	$6$
2	$10$
4	$14$
$-2$	$2$
$-4$	$-2$

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 $\left(-6,6\right)$ of the two graphs. So, the intersection point on the $x$ coordinate is $-6$ .

Thus, the value of $x$ is $-6$