Question
How can you interpret the inequality?
-9s ≤ -18
-9 times s is less than or equal to -18
-9 times s is greater than -18
-9 times s is greater than or equal to -18
-9 times s is less than -18
Excellent!
To solve the inequality, first solve for the value of s that makes the associated equation true. That will give you the boundary point for the inequality. Solve on paper or show your work below. Then, enter your answer on Zearn.
-9s ≤ -18
−9s
=
−18
s
=
Good work!
2 is the solution to the equation and the boundary point for the inequality. Is 2 also a solution to the inequality?
-9s ≤ -18
-9s = -18
s = 2
Yes
No
You got it!
You found that 2 is the boundary point and is also a solution to the inequality. How can you represent this on a number line?
-9s ≤ -18
-9s = -18
s = 2
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
Excellent!
Now test one value less than the boundary, like 1, and one value greater than the boundary, like 3. Does each of these values for s make the inequality true or false? Complete the table.
-9s ≤ -18
-9s = -18
s = 2
s= 1 s= 2 (boundary) s= 3
-9s ≤ -18
Answers
GPT-4o mini
Let's evaluate the inequality -9s ≤ -18 for the values s = 1 and s = 3, as you have mentioned.
1. **For s = 1:**
\[
-9(1) \leq -18 \implies -9 \leq -18 \quad \text{(False)}
\]
2. **For s = 2:**
\[
-9(2) \leq -18 \implies -18 \leq -18 \quad \text{(True)}
\]
3. **For s = 3:**
\[
-9(3) \leq -18 \implies -27 \leq -18 \quad \text{(False)}
\]
Now, let's summarize the results in a table format:
| s | -9s | -9s ≤ -18 | True/False |
|-----|--------------|-------------|-------------|
| 1 | -9 | -9 ≤ -18 | False |
| 2 | -18 | -18 ≤ -18 | True |
| 3 | -27 | -27 ≤ -18 | False |
So, to conclude:
- The value \( s = 2 \) is the boundary point, and it satisfies the inequality.
- The values less than 2 (e.g., s = 1) do not satisfy the inequality.
- The values greater than 2 (e.g., s = 3) also do not satisfy the inequality.
The solution to the inequality, therefore, includes all values of \( s \) that are less than or equal to 2. You can express this using interval notation as \( (-\infty, 2] \).
1. **For s = 1:**
\[
-9(1) \leq -18 \implies -9 \leq -18 \quad \text{(False)}
\]
2. **For s = 2:**
\[
-9(2) \leq -18 \implies -18 \leq -18 \quad \text{(True)}
\]
3. **For s = 3:**
\[
-9(3) \leq -18 \implies -27 \leq -18 \quad \text{(False)}
\]
Now, let's summarize the results in a table format:
| s | -9s | -9s ≤ -18 | True/False |
|-----|--------------|-------------|-------------|
| 1 | -9 | -9 ≤ -18 | False |
| 2 | -18 | -18 ≤ -18 | True |
| 3 | -27 | -27 ≤ -18 | False |
So, to conclude:
- The value \( s = 2 \) is the boundary point, and it satisfies the inequality.
- The values less than 2 (e.g., s = 1) do not satisfy the inequality.
- The values greater than 2 (e.g., s = 3) also do not satisfy the inequality.
The solution to the inequality, therefore, includes all values of \( s \) that are less than or equal to 2. You can express this using interval notation as \( (-\infty, 2] \).