Answer
The solution of the equation is $x=5$.
The graph is shown below.
Work Step by Step
The given equation is
$\Rightarrow |x-6|=|-x+4|$
Write related linear equations.
$\Rightarrow x-6=-x+4$ ...... (1)
$\Rightarrow x-6=-(-x+4)$ ...... (2)
Solve equation (1).
$\Rightarrow x-6=-x+4$
Write a system of linear equations using each side of the original equation.
$\Rightarrow y=x-6$
$\Rightarrow y=-x+4$
By using graphing calculator graph the system.
The intersection point is $(5,-1)$.
Check:
$\Rightarrow |x-6|=|-x+4|$
$\Rightarrow |5-6|=|-5+4|$
$\Rightarrow |-1|=|-1|$
$\Rightarrow 1=1$
True.
Solve equation (2).
$\Rightarrow x-6=-(-x+4)$
Write a system of linear equations using each side of the original equation.
$\Rightarrow y=x-6$
$\Rightarrow y=-(-x+4)$
By using graphing calculator graph the system.
Both lines are parallel. There is no solution.
Hence, the solution of the equation is $x=5$.
