Question

solve and graph the inequality. Choose the answer below. −3.6(4.5n−1.7)<−6.4n+39.44

Answer 1

To solve the inequality \(-3.6(4.5n - 1.7) < -6.4n + 39.44\), follow these steps:

1. **Distribute the \(-3.6\)** on the left side:
\[
-3.6 \cdot 4.5n + 3.6 \cdot 1.7 < -6.4n + 39.44
\]
This simplifies to:
\[
-16.2n + 6.12 < -6.4n + 39.44
\]

2. **Add \(6.4n\) to both sides** to gather the \(n\) terms:
\[
-16.2n + 6.4n + 6.12 < 39.44
\]
This simplifies to:
\[
-9.8n + 6.12 < 39.44
\]

3. **Subtract \(6.12\) from both sides**:
\[
-9.8n < 39.44 - 6.12
\]
This simplifies to:
\[
-9.8n < 33.32
\]

4. **Divide by \(-9.8\)**, remembering to flip the inequality sign:
\[
n > \frac{33.32}{-9.8}
\]
This simplifies to:
\[
n > -3.4
\]

Now we have the solution \(n > -3.4\).

To graph the inequality:
- Draw a number line.
- Place a circle at \(-3.4\) (open circle because \(n\) does not include \(-3.4\)).
- Shade to the right of \(-3.4\) to indicate all numbers greater than \(-3.4\).

Thus, the final solution is \(n > -3.4\), and the graph represents this solution visually.