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Expert-verified Found in: Page 29 ### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465 # In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.$\frac{x+1}{3 }+\frac{x+2}{7}=5$

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

## Step 1. Given information.

We have:

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

## Step 2. Solve the equation algebraically.

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

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

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

$\frac{x+1}{3}· 21+\frac{x+2}{7}· 21=5· 21\phantom{\rule{0ex}{0ex}}7\left(x+1\right)+3\left(x+2\right)=105\phantom{\rule{0ex}{0ex}}7x+7+3x+6=105\phantom{\rule{0ex}{0ex}}10x+13=105$

Subtract $13$ to both sides:

$10x+13-13=105-13\phantom{\rule{0ex}{0ex}}10x=92\phantom{\rule{0ex}{0ex}}\frac{10x}{10}=\frac{92}{10}\phantom{\rule{0ex}{0ex}}x=\frac{46}{5}$

## 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 $\frac{x+1}{3 }+\frac{x+2}{7}=5$ using the graphing utility:  ### Want to see more solutions like these? 