Let's simplify the expression step by step.
The expression given is:
\[ -\frac{2}{3}\left(\frac{1}{3}g - \frac{3}{4}\right) - 10g \]
- Distribute \(-\frac{2}{3}\) to the terms inside the parentheses:
\[ -\frac{2}{3} \cdot \frac{1}{3}g + \frac{2}{3} \cdot \frac{3}{4} \]
Calculating \(-\frac{2}{3} \cdot \frac{1}{3}g\):
\[ -\frac{2}{9}g \]
Now calculating \(\frac{2}{3} \cdot \frac{3}{4}\):
\[ \frac{2 \cdot 3}{3 \cdot 4} = \frac{6}{12} = \frac{1}{2} \]
So, the expression becomes:
\[ -\frac{2}{9}g + \frac{1}{2} - 10g \]
- Combine the \(g\) terms:
To combine \(-\frac{2}{9}g\) with \(-10g\), we need a common denominator. The common denominator for 9 and 1 (denominator of 10) is 9.
Express \(-10g\) with a denominator of 9:
\[ -10g = -\frac{90}{9}g \]
Now we can combine:
\[ -\frac{2}{9}g - \frac{90}{9}g = -\frac{92}{9}g \]
- Put it all together:
Now, combine \(-\frac{92}{9}g\) with \(\frac{1}{2}\):
The expression is now:
\[ -\frac{92}{9}g + \frac{1}{2} \]
To combine these two terms, we need a common denominator for \(\frac{1}{2}\) and \(-\frac{92}{9}g\). The common denominator is 18.
Convert \(\frac{1}{2}\):
\[ \frac{1}{2} = \frac{9}{18} \]
Thus, the final expression is:
\[ -\frac{92}{9}g + \frac{9}{18} = -\frac{92}{9}g + \frac{9}{18} \]
This cannot be further simplified meaningfully since they are not like terms.
Therefore, the final expression is:
\[ -\frac{92}{9}g + \frac{9}{18} \]
This can also be represented as:
\[ -\frac{92}{9}g + \frac{1}{2} \]
So, the simplified result is:
\[ -\frac{92}{9}g + \frac{1}{2} \]
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