Question

Solve and graph the inequality. Choose the answer below.

−3.6(4.5n−1.7)<−6.4n+39.44

(2 points)
Responses

Answer 1

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

1. Distribute \(-3.6\) on the left side:

\[
-3.6 \cdot 4.5n + 3.6 \cdot 1.7 < -6.4n + 39.44
\]

This becomes:

\[
-16.2n + 6.12 < -6.4n + 39.44
\]

2. Next, isolate the terms involving \(n\) on one side. To do this, add \(16.2n\) to both sides:

\[
6.12 < 9.8n + 39.44
\]

3. Now, subtract \(39.44\) from both sides:

\[
6.12 - 39.44 < 9.8n
\]

This simplifies to:

\[
-33.32 < 9.8n
\]

4. Finally, divide both sides by \(9.8\):

\[
\frac{-33.32}{9.8} < n
\]

Calculating \(\frac{-33.32}{9.8}\):

\[
\approx -3.4
\]

So the inequality simplifies to:

\[
n > -3.4
\]

### Graphing the Inequality

To graph the inequality \(n > -3.4\), you would:

- Draw a number line.
- Locate \(-3.4\) on the number line.
- Since the inequality is strict (greater than), draw an open circle at \(-3.4\).
- Shade the region to the right of \(-3.4\), indicating that all numbers greater than \(-3.4\) satisfy the inequality.

### Summary

The solution to the inequality is:

\[
n > -3.4
\]

And the graph consists of an open circle at \(-3.4\) with shading to the right.