Question

Use the graphical method to solve the equation in the indicated exercise form the Section 1.5. (Lesson 1.11)

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

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.

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

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

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

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 $\left(4,4\right)$.

So, the solution is $x=4$.