Chapter 1.9, Problem 31E

To determine

To calculate: The value of $x$ from the equation $x-4=5x+12$ by algebraic method and graphical method.

Answer to Problem 31E

The value of $x$ is $-4$ and Graph of the equation is provided below,

  

Explanation of Solution

Given information:

The equation $x-4=5x+12$ .

Calculation:

It is provided that the equation $x-4=5x+12$ .

Algebraic method;

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

Subtract $-x$ from the equation $x-4=5x+12$ ,

  $\begin{array}{c}-x+x-4=5x-x+12\\ -4=4x+12\end{array}$

Subtract -12 from the equation,

  $\begin{array}{c}-4-12=4x+12-12\\ -16=4x\\ -4=x\end{array}$

Therefore, the value of $x=-4$ .

Graphical method;

Let put $y_1=x-4$ and $y_2=5x+12$

The graph of the equation $y_1=x-4$ can be sketched using the table,

$x$	$y$
0	$-4$
2	$-2$
4	$0$
$-2$	$-7$
$-4$	$-8$

The graph of equation is provided below,

  

The graph of the equation $y_2=5x+12$ can be sketched using the table,

$x$	$y$
0	$12$
2	$22$
4	$32$
$-2$	$2$
$-4$	$-8$

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 $\left(-4,8\right)$ of the two graphs. So, the intersection point on the $x$ coordinate is $-4$ .

Thus, the value of $x$ is $-4$