Question

Solve the inequality.
How can you interpret the inequality?
-8q ≥ -64

-8 times q is less than -64

-8 times q is greater than or equal to -64

-8 times q is greater than -64

-8 times q is less than or equal to -64
Great job!
To solve the inequality, first solve for the value of q 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.
-8q ≥ -64
−8q
=
−64

q
=
Nice!
8 is the solution to the equation and the boundary point for the inequality. Is 8 also a solution to the inequality?
-8q ≥ -64

-8q = -64
q = 8

Yes

No
Great job!
You found that 8 is the boundary point and is also a solution to the inequality. How can you represent this on a number line?
-8q ≥ -64

-8q = -64
q = 8

7
8
9
10
11
12
13
14

7
8
9
10
11
12
13
14
Excellent!
Now test one value less than the boundary, like 7, and one value greater than the boundary, like 9. Does each of these values for q make the inequality true or false? Complete the table.
-8q ≥ -64

-8q = -64
q = 8
q= 7 q= 8 (boundary) q= 9
-8q ≥ -64
true

Answer 1

Let's go through the steps to solve the inequality and test the values:

1. **Solve the inequality**:
\[
-8q \geq -64
\]
To isolate \(q\), we can divide both sides by \(-8\). Remember that when dividing or multiplying by a negative number, the inequality sign flips. Therefore:
\[
q \leq \frac{-64}{-8}
\]
\[
q \leq 8
\]

2. **Interpretation**:
The correct interpretation of the original inequality \(-8q \geq -64\) is:
-8 times \(q\) is **greater than or equal to** -64.

3. **Boundary Point**:
The boundary point is \(q = 8\). Because the inequality is \(q \leq 8\), 8 is included in the solution set.

4. **Testing Values**:
Now we test the values \(q = 7\) and \(q = 9\):

- For \(q = 7\):
\[
-8(7) = -56
\]
Check: \(-56 \geq -64\) (True)

- For \(q = 8\) (boundary point):
\[
-8(8) = -64
\]
Check: \(-64 \geq -64\) (True)

- For \(q = 9\):
\[
-8(9) = -72
\]
Check: \(-72 \geq -64\) (False)

5. **Complete the Table**:

| \(q\) | \(-8q\) | Inequality \( -8q \geq -64 \) |
|-------|---------|-------------------------------|
| 7 | -56 | True |
| 8 | -64 | True |
| 9 | -72 | False |

6. **Conclusion**:
The solution to the inequality is \(q \leq 8\), which means that any value of \(q\) that is less than or equal to 8 satisfies the original inequality. You can represent this on a number line by shading to the left of 8 and including 8 itself (usually represented with a closed dot at 8).