To determine the average atomic mass of element [tex]\(X\)[/tex] given the isotopic masses and their respective abundances, we follow these steps:
1. Convert the percentage abundances to decimal form:
- For isotope 53x: [tex]\(19.61\% = \frac{19.61}{100} = 0.1961\)[/tex]
- For isotope 56x: [tex]\(53.91\% = \frac{53.91}{100} = 0.5391\)[/tex]
- For isotope 58x: [tex]\(26.48\% = \frac{26.48}{100} = 0.2648\)[/tex]
2. Multiply each isotope's mass by its respective decimal abundance:
- For isotope 53x: [tex]\(0.1961 \times 52.62 = 10.307082\)[/tex]
- For isotope 56x: [tex]\(0.5391 \times 56.29 = 30.353439\)[/tex]
- For isotope 58x: [tex]\(0.2648 \times 58.31 = 15.444688\)[/tex]
3. Sum the results from step 2 to find the average atomic mass:
[tex]\[
10.307082 + 30.353439 + 15.444688 = 56.105209
\][/tex]
Thus, the average atomic mass of element [tex]\(X\)[/tex] is approximately [tex]\(56.11 \, \text{amu}\)[/tex].
So the final answer to the question is:
[tex]\[
\boxed{56.11}
\][/tex]
