Question
1. Which of the following values for b makes the inequality −32.5 − 6b ≥48.5
true?(2 points)
Responses
-12.5
-12.5
-13.5
-13.5
-12
-12
-12
-12
Question 2
2. Which set expresses the solution to the compound inequality −2≤2x+13−4<1
?(2 points)
Responses
{x: 3≤x<7}
{x: 3≤x<7}
{x: 52≤x<7}
{x: 52≤x<7}
{x: −32≤x<1}
{x: −32≤x<1}
{x: 52≤x<1}
{x: 52≤x<1}
Question 3
3. Which option is the solution to the inequality −12g+18>−5g+53
?(2 points)
Responses
g<−5
g<−5
g<71−17
g<71−17
g>71−17
g is greater than 71 over negative 17
g>−5
g is greater than negative 5
Question 4
4. Graph x≤−3
.(2 points)
Responses
Question 5
5. Find the solution set of 4x−3>9
and x+6>−2
.(2 points)
Responses
The solution set is null
The solution set is null
{x | x>3}
{x | x>3}
{3, −8}
{3, −8}
{x | x>−8}
{x | x>−8}
Question 6
6. Select the solution set represented on the graph.
(2 points)
Responses
x≤−3 or x>1
x≤−3 or x>1
x≤−3 or x≥1
x≤−3 or x≥1
x<−3 or x>1
x<−3 or x>1
x<−3 and x>1
x<−3 and x>1
Question 7
7. Solve the inequality 25m−7≤17
.(2 points)
The solution to the inequality is
Make sure your variable is on the left.
true?(2 points)
Responses
-12.5
-12.5
-13.5
-13.5
-12
-12
-12
-12
Question 2
2. Which set expresses the solution to the compound inequality −2≤2x+13−4<1
?(2 points)
Responses
{x: 3≤x<7}
{x: 3≤x<7}
{x: 52≤x<7}
{x: 52≤x<7}
{x: −32≤x<1}
{x: −32≤x<1}
{x: 52≤x<1}
{x: 52≤x<1}
Question 3
3. Which option is the solution to the inequality −12g+18>−5g+53
?(2 points)
Responses
g<−5
g<−5
g<71−17
g<71−17
g>71−17
g is greater than 71 over negative 17
g>−5
g is greater than negative 5
Question 4
4. Graph x≤−3
.(2 points)
Responses
Question 5
5. Find the solution set of 4x−3>9
and x+6>−2
.(2 points)
Responses
The solution set is null
The solution set is null
{x | x>3}
{x | x>3}
{3, −8}
{3, −8}
{x | x>−8}
{x | x>−8}
Question 6
6. Select the solution set represented on the graph.
(2 points)
Responses
x≤−3 or x>1
x≤−3 or x>1
x≤−3 or x≥1
x≤−3 or x≥1
x<−3 or x>1
x<−3 or x>1
x<−3 and x>1
x<−3 and x>1
Question 7
7. Solve the inequality 25m−7≤17
.(2 points)
The solution to the inequality is
Make sure your variable is on the left.
Answers
GPT-4o mini
Let's solve each of the questions systematically:
### Question 1
**Which of the following values for b makes the inequality −32.5 − 6b ≥48.5 true?**
1. Start by solving the inequality:
\[
-32.5 - 6b \geq 48.5
\]
Add \(32.5\) to both sides:
\[
-6b \geq 81
\]
Now divide by \(-6\) (remember to reverse the inequality sign):
\[
b \leq -13.5
\]
From the options provided: **-13.5** satisfies this inequality.
### Question 2
**Which set expresses the solution to the compound inequality −2≤2x+13−4<1?**
1. Start by simplifying:
\[
-2 \leq 2x + 9 < 1
\]
2. Break it into two parts:
- For \(-2 \leq 2x + 9\):
\[
-11 \leq 2x \implies -\frac{11}{2} \leq x \implies -5.5 \leq x
\]
- For \(2x + 9 < 1\):
\[
2x < -8 \implies x < -4
\]
Combining gives:
\[
-5.5 \leq x < -4
\]
None of the options match this. Assuming a simpler error, let's check other similar options.
The intended solution seems like it might be the one close to:
\(\{ x : 3 \leq x < 7 \}\)
### Question 3
**Which option is the solution to the inequality −12g + 18 > −5g + 53?**
1. Rearranging we have:
\[
-12g + 5g > 53 - 18
\]
This simplifies to:
\[
-7g > 35
\]
By dividing by \(-7\) (flip inequality):
\[
g < -5
\]
So, the solution is **g < -5**.
### Question 4
**Graph \(x \leq -3\)**
This is a simple inequality, and the corresponding graph would be a line on the number line that starts at -3 (included) and goes leftwards to negative infinity.
### Question 5
**Find the solution set of \(4x - 3 > 9\) and \(x + 6 > -2\)**
1. Solve \(4x - 3 > 9\):
\[
4x > 12 \implies x > 3
\]
2. Solve \(x + 6 > -2\):
\[
x > -8
\]
The solution set would be \(x > 3\) since it's the more restrictive condition.
Thus the answer is: **{x | x > 3}**.
### Question 6
**Select the solution set represented on the graph.**
Given the possible responses:
- If the graph displays regions where \(x \leq -3\) and \(x > 1\), the correct answer is:
**\(x \leq -3\) or \(x > 1\)**.
### Question 7
**Solve the inequality \(25m - 7 \leq 17\)**.
1. Start by adding \(7\) to both sides:
\[
25m \leq 24
\]
2. Divide by \(25\):
\[
m \leq \frac{24}{25}
\]
So, the solution to the inequality is **m ≤ 24/25**.
### Final Answers Summary
1. -13.5
2. None clearly correct. (Close: {x: 3 ≤ x < 7})
3. g < -5
4. (Graph of x ≤ -3)
5. {x | x > 3}
6. x ≤ -3 or x > 1
7. m ≤ 24/25
### Question 1
**Which of the following values for b makes the inequality −32.5 − 6b ≥48.5 true?**
1. Start by solving the inequality:
\[
-32.5 - 6b \geq 48.5
\]
Add \(32.5\) to both sides:
\[
-6b \geq 81
\]
Now divide by \(-6\) (remember to reverse the inequality sign):
\[
b \leq -13.5
\]
From the options provided: **-13.5** satisfies this inequality.
### Question 2
**Which set expresses the solution to the compound inequality −2≤2x+13−4<1?**
1. Start by simplifying:
\[
-2 \leq 2x + 9 < 1
\]
2. Break it into two parts:
- For \(-2 \leq 2x + 9\):
\[
-11 \leq 2x \implies -\frac{11}{2} \leq x \implies -5.5 \leq x
\]
- For \(2x + 9 < 1\):
\[
2x < -8 \implies x < -4
\]
Combining gives:
\[
-5.5 \leq x < -4
\]
None of the options match this. Assuming a simpler error, let's check other similar options.
The intended solution seems like it might be the one close to:
\(\{ x : 3 \leq x < 7 \}\)
### Question 3
**Which option is the solution to the inequality −12g + 18 > −5g + 53?**
1. Rearranging we have:
\[
-12g + 5g > 53 - 18
\]
This simplifies to:
\[
-7g > 35
\]
By dividing by \(-7\) (flip inequality):
\[
g < -5
\]
So, the solution is **g < -5**.
### Question 4
**Graph \(x \leq -3\)**
This is a simple inequality, and the corresponding graph would be a line on the number line that starts at -3 (included) and goes leftwards to negative infinity.
### Question 5
**Find the solution set of \(4x - 3 > 9\) and \(x + 6 > -2\)**
1. Solve \(4x - 3 > 9\):
\[
4x > 12 \implies x > 3
\]
2. Solve \(x + 6 > -2\):
\[
x > -8
\]
The solution set would be \(x > 3\) since it's the more restrictive condition.
Thus the answer is: **{x | x > 3}**.
### Question 6
**Select the solution set represented on the graph.**
Given the possible responses:
- If the graph displays regions where \(x \leq -3\) and \(x > 1\), the correct answer is:
**\(x \leq -3\) or \(x > 1\)**.
### Question 7
**Solve the inequality \(25m - 7 \leq 17\)**.
1. Start by adding \(7\) to both sides:
\[
25m \leq 24
\]
2. Divide by \(25\):
\[
m \leq \frac{24}{25}
\]
So, the solution to the inequality is **m ≤ 24/25**.
### Final Answers Summary
1. -13.5
2. None clearly correct. (Close: {x: 3 ≤ x < 7})
3. g < -5
4. (Graph of x ≤ -3)
5. {x | x > 3}
6. x ≤ -3 or x > 1
7. m ≤ 24/25