Question

Complete the statement so that it represents the solution to the inequality. Use the table to help you.

x= 8x=9 (boundary)x= 1020 + 60x ≤ 560TrueTrueFalse

x 

 

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Answer 1

To solve the inequality represented by the provided information, we need to clarify the condition it expresses and how the boundary conditions relate to the solution.

Given:
- Boundary points: \(x = 8, x = 9, x = 10\)
- The inequality involves: \(20 + 60x \leq 560\)

Let's start by solving the inequality \(20 + 60x \leq 560\):

1. Subtract 20 from both sides:
\[
60x \leq 540
\]

2. Divide both sides by 60:
\[
x \leq 9
\]

Now, considering the provided information about the boundaries:
- The inequality \(x \leq 9\) suggests that the solution includes all values less than or equal to 9.

Given that:
- \(x = 8\) is true,
- \(x = 9\) is true, and
- \(x = 10\) is false (as it does not satisfy the inequality).

We can formulate the complete statement for the solution to the inequality as:

**The solution to the inequality \(20 + 60x \leq 560\) is \(x \leq 9\).**

To finalize the statement using the gap analysis from your table, you can phrase it as:

**The solution to the inequality is \(x \leq 9\).**

**Therefore, the statement could be completed as:**
- \(x \leq 9\) (with the symbol being "less than or equal to").