Question

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.

$\frac{2x+1}{3}+16=3x$

Short answer

The required solution is $x=7$. The graph of the solution is given below:

Step-by-step solution

Step 1. Given information. 

We have:

$\frac{2x+1}{3}+16=3x$

Step 2. Solve the equation algebraically. 

The equation is $\frac{2x+1}{3}+16=3x$.

Substract $16$from both sides:

$$\begin{gathered} \frac{2x+1}{3}+16-16=3x-16 \\ \frac{2x+1}{3}=3x-16 \end{gathered}$$

Multiply both sides by $3:$

$$\begin{gathered} \frac{2x+1}{3}·\hspace{0.17em}3=3x·\hspace{0.17em}3-16·\hspace{0.17em}3 \\ 2x+1=9x-48 \\ 2x+1-1=9x-48-1 \\ 2x=9x-49 \\ 2x-9x=9x-49-9x \\ -7x=-49 \\ \frac{-7x}{-7}=\frac{-49}{-7} \\ x=7 \end{gathered}$$

Step 3. Verify the solution using a graphing utility. 

The solution of the equation is$x=7.$

Draw the graph of the equation $\frac{2x+1}{3}+16=3x$ using the graphing utility: