Question

Item 4 Solve the equation by graphing. ∣x+1∣=∣−x−9∣

Answer 1

The solution is (-5,4).

Explanation:

We are given the equation, |x+1|=|-x-9|

Now, |x+1| =
`\left\{\begin{matrix}x+1 & ,x>0\\ -(x+1)& ,x<0\end{matrix}\right.`

Also, |-x-9| =
`\left\{\begin{matrix}-x-9 & ,x>0\\ -(-x-9)& ,x<0\end{matrix}\right.`

So, equating these two functions gives the value of x = -5. After substituting this value in any of the function term say y = x+1, we get y = 4.

Moreover, from the graph below we see that, after equating these functions, the solution is given by the points at which they intersect.

Hence, the solution is (x,y) = (-5,4).