Questions: Part 3 of 4 (b) n-8 ≤ -6 and 3/4 n < -3 The solution set is .

Solution Steps

To solve the given system of inequalities, we need to solve each inequality separately and then find the intersection of the solution sets.

1. Solve the first inequality \( n - 8 \leq -6 \).
2. Solve the second inequality \( \frac{3}{4} n < -3 \).
3. Find the intersection of the solution sets from the two inequalities.

To solve the inequality \( n - 8 \leq -6 \), we need to isolate \( n \).

\[ n - 8 \leq -6 \]

Add 8 to both sides:

\[ n - 8 + 8 \leq -6 + 8 \]

\[ n \leq 2 \]

To solve the inequality \( \frac{3}{4} n < -3 \), we need to isolate \( n \).

\[ \frac{3}{4} n < -3 \]

Multiply both sides by the reciprocal of \( \frac{3}{4} \), which is \( \frac{4}{3} \):

\[ \left( \frac{4}{3} \right) \left( \frac{3}{4} n \right) < \left( \frac{4}{3} \right) (-3) \]

\[ n < -4 \]

The solution to the system of inequalities is the intersection of the solutions to the individual inequalities. We have:

\[ n \leq 2 \]

\[ n < -4 \]

The intersection of these two sets is:

\[ n < -4 \]

Final Answer