To simplify and combine like terms in the given expression [tex]\(\frac{11}{12} - \frac{1}{6} q + \frac{5}{6} q - \frac{1}{3}\)[/tex], follow these steps:
1. Identify and separate like terms:
- Constant terms: [tex]\(\frac{11}{12}\)[/tex] and [tex]\(-\frac{1}{3}\)[/tex]
- Terms involving [tex]\(q\)[/tex]: [tex]\(-\frac{1}{6} q\)[/tex] and [tex]\(\frac{5}{6} q\)[/tex]
2. Combine the constant terms:
Convert each constant term to a common denominator to make addition easier.
The least common denominator for [tex]\(\frac{11}{12}\)[/tex] and [tex]\(-\frac{1}{3}\)[/tex] is 12.
[tex]\[
\frac{11}{12} - \frac{1}{3} = \frac{11}{12} - \frac{1 \times 4}{3 \times 4} = \frac{11}{12} - \frac{4}{12}
\][/tex]
Now, combine the fractions:
[tex]\[
\frac{11}{12} - \frac{4}{12} = \frac{11 - 4}{12} = \frac{7}{12}
\][/tex]
3. Combine the terms involving [tex]\(q\)[/tex]:
Both terms [tex]\(-\frac{1}{6} q\)[/tex] and [tex]\(\frac{5}{6} q\)[/tex] already have the same denominator.
[tex]\[
-\frac{1}{6} q + \frac{5}{6} q
\][/tex]
Combine the coefficients:
[tex]\[
-\frac{1}{6} + \frac{5}{6} = \frac{-1 + 5}{6} = \frac{4}{6} = \frac{2}{3}
\][/tex]
So, the combined term involving [tex]\(q\)[/tex] is:
[tex]\[
\frac{2}{3} q
\][/tex]
4. Combine all simplified terms:
The simplified expression, combining the [tex]\(q\)[/tex] term and the constant term, is:
[tex]\[
\frac{2}{3} q + \frac{7}{12}
\][/tex]
Therefore, the equivalent expression after combining like terms is:
[tex]\[
\boxed{\frac{2}{3} q + \frac{7}{12}}
\][/tex]
