Question

solve the given equation for x.
\\(\frac{x}{7} + \frac{x}{2} = \frac{8}{7}\\)

select the correct choice below and, if necessary, fill in the answer box within your choice.
\\(\bigcirc\\) a. \\(x = \square\\) (type an integer or a simplified fraction.)
\\(\bigcirc\\) b. the solution is all real numbers
\\(\bigcirc\\) c. there is no solution

Explanation:

Step1: Find common denominator

The common denominator of 7 and 2 is 14. Rewrite each term:
$\frac{2x}{14} + \frac{7x}{14} = \frac{16}{14}$

Step2: Combine like terms

Add the left-hand side terms:
$\frac{2x + 7x}{14} = \frac{16}{14}$
$\frac{9x}{14} = \frac{16}{14}$

Step3: Eliminate denominator

Multiply both sides by 14:
$9x = 16$

Step4: Solve for x

Divide both sides by 9:
$x = \frac{16}{9}$

Answer:

A. $x=\frac{16}{9}$