Q. 21 - Precalculus Enhanced with Graphing Utilities

Question

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

$\frac{x+1}{3\hspace{0.17em}}+\frac{x+2}{7}=5$

Step-by-Step Solution

Answer

The required solution is $x=\frac{46}{5}$. The graph of the solution is given below:

Step 1. Given information.

We have:

$\frac{x+1}{3\hspace{0.17em}}+\frac{x+2}{7}=5$

Step 2. Solve the equation algebraically.

The equation is $\frac{x+1}{3\hspace{0.17em}}+\frac{x+2}{7}=5$.

Find the least common multiplier of $3,7$:$21$

Multiply by LCM (Least common multiple) to both sides of the equation.

$$\begin{gathered} \frac{x+1}{3}·\hspace{0.17em}21+\frac{x+2}{7}·\hspace{0.17em}21=5·\hspace{0.17em}21 \\ 7\left(x+1\right)+3\left(x+2\right)=105 \\ 7x+7+3x+6=105 \\ 10x+13=105 \end{gathered}$$

Subtract $13$ to both sides:

$$\begin{gathered} 10x+13-13=105-13 \\ 10x=92 \\ \frac{10x}{10}=\frac{92}{10} \\ x=\frac{46}{5} \end{gathered}$$

Step 3. Verify the solution using a graphing utility.

The solution of the equation is $x=\frac{46}{5}$.

Draw the graph of the equation $\frac{x+1}{3\hspace{0.17em}}+\frac{x+2}{7}=5$ using the graphing utility: