Question

Use the graphical method to solve the equation

$\sqrt{5-x}+1=x-2$

Short answer

The solution by graphically method is $x=4$.

Step-by-step solution

Step 1. Definition of the intersection point.

An intersection is a single point where two lines meet or cross each other.

Step 2. Draw the graph of the equation.

$\sqrt{5-x}+1=x-2$

Equate the left side of the given equation to$y_1$and the right side to $y_2$.

$\begin{array}{l}{y}_1=\sqrt{5-x}+1\\ y_2=x-2\end{array}$

Now, equate the left side of the equation to $y$. Then sketch the graph of the equation on a graphing facility

Draw the graph:

Step 3. Solve the equation graphically.

The solutions to the given equations are intersection points.

So, identify whether graphs are intersecting with each other:

As we can see that graphs are intersecting at $\left(4,2\right)$.

So, the solution is $x=4$.