Question
Solve the inequality.
How can you interpret the inequality?
-8q ≥ -64
-8 times q is less than or equal to -64
-8 times q is less than -64
-8 times q is greater than -64
-8 times q is greater than or equal to -64
You got it!
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
=
Excellent!
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
7
8
9
10
11
12
13
14
Nice!
Draw a number line to represent your inequality.
-8q ≥ -64
q= 7 q= 8 (boundary) q= 9
-8q ≥ -64 true true false
7
8
9
10
11
12
13
14
7
8
9
10
11
12
13
14
Nice!
Now use your number line to write the solution to the inequality.
-8q ≥ -64
q
How can you interpret the inequality?
-8q ≥ -64
-8 times q is less than or equal to -64
-8 times q is less than -64
-8 times q is greater than -64
-8 times q is greater than or equal to -64
You got it!
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
=
Excellent!
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
7
8
9
10
11
12
13
14
Nice!
Draw a number line to represent your inequality.
-8q ≥ -64
q= 7 q= 8 (boundary) q= 9
-8q ≥ -64 true true false
7
8
9
10
11
12
13
14
7
8
9
10
11
12
13
14
Nice!
Now use your number line to write the solution to the inequality.
-8q ≥ -64
q
Answers
GPT-4o mini
To solve the inequality \(-8q \geq -64\), we need to isolate the variable \(q\).
1. **Divide both sides by -8**: Remember to reverse the inequality sign when dividing by a negative number.
\[
q \leq \frac{-64}{-8}
\]
2. **Calculate the right side**:
\[
q \leq 8
\]
So, the solution to the inequality is \(q \leq 8\).
### Interpretation of the Inequality
The inequality \(q \leq 8\) means that \(q\) can be any value that is less than or equal to 8.
### Boundary Point
The boundary point here is 8, which is included in the solution.
### Testing Values
- When we test \(q = 7\):
\[
-8(7) = -56 \quad \text{and} \quad -56 \geq -64 \quad \text{(True)}
\]
- When we test \(q = 8\):
\[
-8(8) = -64 \quad \text{and} \quad -64 \geq -64 \quad \text{(True)}
\]
- When we test \(q = 9\):
\[
-8(9) = -72 \quad \text{and} \quad -72 \geq -64 \quad \text{(False)}
\]
### Number Line
To represent \(q \leq 8\) on a number line, you would place a closed circle on 8 (indicating that 8 is included in the solution) and shade everything to the left of 8.
### Final Solution
The solution to the inequality is:
\[
q \leq 8
\]
1. **Divide both sides by -8**: Remember to reverse the inequality sign when dividing by a negative number.
\[
q \leq \frac{-64}{-8}
\]
2. **Calculate the right side**:
\[
q \leq 8
\]
So, the solution to the inequality is \(q \leq 8\).
### Interpretation of the Inequality
The inequality \(q \leq 8\) means that \(q\) can be any value that is less than or equal to 8.
### Boundary Point
The boundary point here is 8, which is included in the solution.
### Testing Values
- When we test \(q = 7\):
\[
-8(7) = -56 \quad \text{and} \quad -56 \geq -64 \quad \text{(True)}
\]
- When we test \(q = 8\):
\[
-8(8) = -64 \quad \text{and} \quad -64 \geq -64 \quad \text{(True)}
\]
- When we test \(q = 9\):
\[
-8(9) = -72 \quad \text{and} \quad -72 \geq -64 \quad \text{(False)}
\]
### Number Line
To represent \(q \leq 8\) on a number line, you would place a closed circle on 8 (indicating that 8 is included in the solution) and shade everything to the left of 8.
### Final Solution
The solution to the inequality is:
\[
q \leq 8
\]