Question

solve and check. \\(\frac{5}{9}n = 15\\) the solution is \\(n = \square\\). (simplify your answer)

Explanation:

Step1: Isolate the variable \( n \)

To solve for \( n \) in the equation \( \frac{5}{9}n = 15 \), we multiply both sides of the equation by the reciprocal of \( \frac{5}{9} \), which is \( \frac{9}{5} \).
\[
n = 15\times\frac{9}{5}
\]

Step2: Simplify the right - hand side

First, we can simplify \( 15\div5 = 3 \), then multiply \( 3\times9 \).
\[
n=3\times9 = 27
\]

Step3: Check the solution

Substitute \( n = 27 \) back into the original equation:
Left - hand side: \( \frac{5}{9}\times27=\frac{5\times27}{9}=5\times3 = 15 \)
Right - hand side: \( 15 \)
Since the left - hand side equals the right - hand side, the solution is correct.

Answer:

\( n = 27 \)