To find an equivalent sum or difference for the expression [tex]\(\frac{11 + 2x}{6}\)[/tex], we can separate the terms in the numerator and divide each term by the denominator individually. This process is known as splitting the fraction.
The original expression is:
[tex]\[
\frac{11 + 2x}{6}
\][/tex]
We will rewrite this as the sum of two separate fractions:
[tex]\[
\frac{11 + 2x}{6} = \frac{11}{6} + \frac{2x}{6}
\][/tex]
Next, we simplify each fraction individually:
[tex]\[
\frac{11}{6} \quad \text{(this fraction is already in its simplest form)}
\][/tex]
[tex]\[
\frac{2x}{6} = \frac{2}{6} x = \frac{1}{3} x
\][/tex]
So, the expression [tex]\(\frac{11 + 2x}{6}\)[/tex] can be rewritten as:
[tex]\[
\frac{11}{6} + \frac{1}{3} x
\][/tex]
Therefore, the equivalent sum for the given expression [tex]\(\frac{11 + 2x}{6}\)[/tex] is:
[tex]\[
\frac{11}{6} + \frac{1}{3} x
\][/tex]
