To evaluate and simplify the expression [tex]\(\frac{10x + y}{4x}\)[/tex] when [tex]\(x = 2\)[/tex] and [tex]\(y = 1\)[/tex], follow these steps:
1. Substitute the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] into the expression:
[tex]\[
\frac{10(2) + 1}{4(2)}
\][/tex]
2. Calculate the numerator:
[tex]\[
10(2) + 1 = 20 + 1 = 21
\][/tex]
3. Calculate the denominator:
[tex]\[
4(2) = 8
\][/tex]
4. Form the new fraction with the calculated values:
[tex]\[
\frac{21}{8}
\][/tex]
5. Simplify the fraction (if possible):
In this case, [tex]\(\frac{21}{8}\)[/tex] cannot be simplified further because 21 and 8 have no common factors other than 1.
6. Convert the fraction to a decimal (if needed):
Performing the division gives:
[tex]\[
\frac{21}{8} = 2.625
\][/tex]
Therefore, the evaluated and simplified expression is:
[tex]\[
\frac{10x + y}{4x} = \frac{21}{8} = 2.625
\][/tex]
