7. $$ \left(\frac{\gamma}{2} \pm \frac{3}{20}\right)-\frac{2}{20} $$

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UpStudy AI · Accepted Answer

Sure, let's simplify the expression step by step:

$$
\left(\frac{\gamma}{2} \pm \frac{3}{20}\right) - \frac{2}{20}
$$

This expression involves a "±" (plus-minus) sign, which means there are two cases to consider:

1. **Plus Case (+):**
   
   $$
   \frac{\gamma}{2} + \frac{3}{20} - \frac{2}{20}
   $$
   
   Combine the constants:
   
   $$
   \frac{3}{20} - \frac{2}{20} = \frac{1}{20}
   $$
   
   So, the expression simplifies to:
   
   $$
   \frac{\gamma}{2} + \frac{1}{20}
   $$

2. **Minus Case (−):**
   
   $$
   \frac{\gamma}{2} - \frac{3}{20} - \frac{2}{20}
   $$
   
   Combine the constants:
   
   $$
   -\frac{3}{20} - \frac{2}{20} = -\frac{5}{20} = -\frac{1}{4}
   $$
   
   So, the expression simplifies to:
   
   $$
   \frac{\gamma}{2} - \frac{1}{4}
   $$

**Final Simplified Expressions:**

$$
\begin{cases}
\frac{\gamma}{2} + \frac{1}{20} \quad &\text{(Plus Case)} \
\frac{\gamma}{2} - \frac{1}{4} \quad &\text{(Minus Case)}
\end{cases}
$$

**Summary:**

$$
\left(\frac{\gamma}{2} \pm \frac{3}{20}\right) - \frac{2}{20} = 
\begin{cases}
\frac{\gamma}{2} + \frac{1}{20} \
\frac{\gamma}{2} - \frac{1}{4}
\end{cases}
$$
$$ \left(\frac{\gamma}{2} \pm \frac{3}{20}\right) - \frac{2}{20} = \begin{cases} \frac{\gamma}{2} + \frac{1}{20} \ \frac{\gamma}{2} - \frac{1}{4} \end{cases} $$

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