Let's solve the rational equation [tex]\(\frac{27}{9} = \frac{3x}{9}\)[/tex] step-by-step.
1. Simplify the left-hand side of the equation:
[tex]\[
\frac{27}{9} = 3
\][/tex]
2. Rewrite the equation with the simplified left-hand side:
[tex]\[
3 = \frac{3x}{9}
\][/tex]
3. Isolate [tex]\(3x\)[/tex] by multiplying both sides of the equation by 9:
[tex]\[
3 \times 9 = 3x
\][/tex]
[tex]\[
27 = 3x
\][/tex]
4. Solve for [tex]\(x\)[/tex] by dividing both sides of the equation by 3:
[tex]\[
\frac{27}{3} = x
\][/tex]
[tex]\[
x = 9
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] in the equation [tex]\(\frac{27}{9} = \frac{3x}{9}\)[/tex] is [tex]\( \boxed{9} \)[/tex].
