Answer
The solution of the equation is $x=-5$.
Work Step by Step
The given equation is
$\Rightarrow |x+1|=|-x-9|$
Write related linear equations.
$\Rightarrow x+1=-x-9$ ...... (1)
$\Rightarrow x+1=-(-x-9)$ ...... (2)
Solve equation (1).
$\Rightarrow x+1=-x-9$
Write a system of linear equations using each side of the original equation.
$\Rightarrow y=x+1$
$\Rightarrow y=-x-9$
By using graphing calculator graph the system.
The intersection point is $(-5,-4)$.
Check:
$\Rightarrow x+1=-x-9$
$\Rightarrow -5+1=-(-5)-9$
$\Rightarrow -5+1=5-9$
$\Rightarrow -4=-4$
True.
Solve equation (2).
$\Rightarrow x+1=-(-x-9)$
Write a system of linear equations using each side of the original equation.
$\Rightarrow y=x+1$
$\Rightarrow y=-(-x-9)$
By using graphing calculator graph the system. Both lines are parallel. The system has no solution.
Hence, the solution of the equation is $x=-5$.
