Question

Solve x9+3≤11
. Graph the solution(1 point)
The solution is x≤

Question 2
Graph the solution (1 point)
Responses

Answer 1

To solve the inequality \( x^9 + 3 \leq 11 \):

1. Start by isolating \( x^9 \):
\[
x^9 + 3 \leq 11
\]
Subtract 3 from both sides:
\[
x^9 \leq 8
\]

2. Next, take the ninth root of both sides:
\[
x \leq 8^{1/9}
\]

3. Evaluating \( 8^{1/9} \):
\[
8 = 2^3 \Rightarrow 8^{1/9} = (2^3)^{1/9} = 2^{3/9} = 2^{1/3}
\]
The numerical value of \( 2^{1/3} \) is approximately \( 1.26 \).

So, the solution is:
\[
x \leq 2^{1/3} \quad \text{or approximately} \quad x \leq 1.26
\]

### Graphing the solution:

To graph the solution, you would:

- Draw a number line.
- Mark the point approximately at \( 1.26 \).
- Shade to the left of \( 1.26 \) to indicate that the solution includes all values less than or equal to \( 1.26 \).

The graph would look like this:

```
<---|---|---|---|---|---|---|---|---|---|--->
0 1 2 3 4 5 6 7 8
●---------------------->
```
(Where "●" indicates \( 1.26 \) is included in the solution).