An absolute value equation in the form |ax+b|=|cx+d| has two related equations.
Equation1: ax+b&= cx+d
Equation2: ax+b&=-(cx+d)
In this case, we are given the equation |x+1|=|- x-9|. Let's split it into the two cases.
Equation1: x+1&= - x-9
Equation2: x+1&=-(- x-9)
Now, let's solve each equation separately.
First Equation
To graph the equation x+1=- x-9, we will create two functions out of the left- and right-hand sides of the equation.
y=x+1 and y=- x -9
The x-coordinate where the graphs of these equations intersect is the solution to our equation.
The graphs intersect at x=-5, which is our solution. Let's check whether it is correct by substituting it into the original equation.
