Chapter 8.6, Problem 5LC

Solution

To identify: The error and describe and correct the error made in solving the equation.

  

The solution is $x=\frac{161}{9}$ .

Given information:

  

Explanation:

Consider the given information.

Error is in second step.

That is $\frac{14}{x+7}=\frac{28}{x}$ is wrong

Here numerator and denominators are added.

it is wrong because $\frac{5}{x},\frac{9}{7}$ have different denominator, so you cannot add the numerators.

Correction

LCM of $\frac{5}{x},\frac{9}{7}$ is $7x$

Multiply the equation on both side by $7x$ .

  $\left(\frac{5}{x}+\frac{9}{7}\right)7x=\frac{28}{x}\cdot 7x$

Remove the parenthesis by using distributive property.

  $\begin{array}{c}\left(\frac{5}{x}+\frac{9}{7}\right)7x=\frac{28}{x}\cdot 7x\\ \frac{5}{x}\cdot 7x+\frac{9}{7}\cdot 7x=\frac{28}{x}\cdot 7x\\ 35+9x=196\end{array}$

Subtract from both sides.

  $\begin{array}{l}9x=196-15\\ 9x=161\\ x=\frac{161}{9}\end{array}$

Hence the solution is $x=\frac{161}{9}$