Question

perfrom the indicated operations and simplify:
\\(\frac{1}{7}x + \frac{1}{11}(x + 17)\\)
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Explanation:

Step1: Distribute the fraction

We use the distributive property \(a(b + c)=ab+ac\) to expand \(\frac{1}{11}(x + 17)\).
\(\frac{1}{11}(x + 17)=\frac{1}{11}x+\frac{17}{11}\)
So the original expression \(\frac{1}{7}x+\frac{1}{11}(x + 17)\) becomes \(\frac{1}{7}x+\frac{1}{11}x+\frac{17}{11}\)

Step2: Combine like terms (x - terms)

To combine \(\frac{1}{7}x\) and \(\frac{1}{11}x\), we find a common denominator for the coefficients. The least common denominator of 7 and 11 is \(7\times11 = 77\).
\(\frac{1}{7}x=\frac{1\times11}{7\times11}x=\frac{11}{77}x\)
\(\frac{1}{11}x=\frac{1\times7}{11\times7}x=\frac{7}{77}x\)
Adding these together: \(\frac{11}{77}x+\frac{7}{77}x=\frac{11 + 7}{77}x=\frac{18}{77}x\)

Step3: Write the final expression

Now we combine the \(x\) - term and the constant term. The expression is \(\frac{18}{77}x+\frac{17}{11}\)

Answer:

\(\frac{18}{77}x+\frac{17}{11}\)