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Q. 21

Expert-verifiedFound in: Page 29

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.

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

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

We have:

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

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.

$\frac{x+1}{3}\xb7\hspace{0.17em}21+\frac{x+2}{7}\xb7\hspace{0.17em}21=5\xb7\hspace{0.17em}21\phantom{\rule{0ex}{0ex}}7\left(x+1\right)+3\left(x+2\right)=105\phantom{\rule{0ex}{0ex}}7x+7+3x+6=105\phantom{\rule{0ex}{0ex}}10x+13=105$

Subtract $13$ to both sides:

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

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:

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