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.
Skip to navigation
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.
Skip to navigation
Answers
GPT-4o mini
Let's solve each question one by one.
### Question 1
**Inequality:** \( -32.5 - 6b \geq 48.5 \)
1. Add \(32.5\) to both sides:
\[
-6b \geq 48.5 + 32.5
\]
\[
-6b \geq 81
\]
2. Divide by \(-6\) (remember to reverse the inequality sign):
\[
b \leq -\frac{81}{6} = -13.5
\]
Thus, the **correct value for \(b\)** is **-13.5**.
### Question 2
**Compound Inequality:** \( -2 \leq 2x + 13 - 4 < 1 \)
1. Simplify:
\[
-2 \leq 2x + 9 < 1
\]
2. Split into two inequalities:
\[
-2 \leq 2x + 9 \quad \text{and} \quad 2x + 9 < 1
\]
3. Solve the first inequality:
\[
-2 - 9 \leq 2x
\]
\[
-11 \leq 2x \implies x \geq -\frac{11}{2} = -5.5
\]
4. Solve the second inequality:
\[
2x + 9 < 1 \implies 2x < 1 - 9 \implies 2x < -8
\]
\[
x < -4
\]
5. Combine the results:
\[
-5.5 \leq x < -4
\]
The closest set from the options reflecting this inequality is **{x: -5.5 ≤ x < -4}**, however, it seems it isn't listed. The correct option should be checked according to the available responses.
### Question 3
**Inequality:** \( -12g + 18 > -5g + 53 \)
1. Rearrange the inequality:
\[
-12g + 5g > 53 - 18
\]
\[
-7g > 35
\]
2. Divide by \(-7\) (reverse the inequality):
\[
g < -5
\]
The solution is **g < -5**.
### Question 4
**Graph:** \( x \leq -3 \)
To graph this inequality, you would draw a number line, place a closed dot (since -3 is included) on -3, and shade to the left to indicate all values less than or equal to -3.
### Question 5
1. Solve \( 4x - 3 > 9 \):
\[
4x > 12 \implies x > 3
\]
2. Solve \( x + 6 > -2 \):
\[
x > -8
\]
The solution set is the intersection of the two results, which is \( x > 3 \).
Thus, the response should be **{x | x > 3}**.
### Question 6
Based on the given options and graphs, if the graph indicates values where \(x \leq -3\) or \(x > 1\), then the appropriate choice would be **\(x \leq -3\) or \(x > 1\)**.
### Question 7
**Inequality:** \( 25m - 7 \leq 17 \)
1. Add \(7\) to both sides:
\[
25m \leq 24
\]
2. Divide by \(25\):
\[
m \leq \frac{24}{25}
\]
So the solution to the inequality is **\( m \leq \frac{24}{25} \)**, which can be expressed as \( m \leq 0.96 \).
If you need any more clarification or specific formatting for responses, let me know!
### Question 1
**Inequality:** \( -32.5 - 6b \geq 48.5 \)
1. Add \(32.5\) to both sides:
\[
-6b \geq 48.5 + 32.5
\]
\[
-6b \geq 81
\]
2. Divide by \(-6\) (remember to reverse the inequality sign):
\[
b \leq -\frac{81}{6} = -13.5
\]
Thus, the **correct value for \(b\)** is **-13.5**.
### Question 2
**Compound Inequality:** \( -2 \leq 2x + 13 - 4 < 1 \)
1. Simplify:
\[
-2 \leq 2x + 9 < 1
\]
2. Split into two inequalities:
\[
-2 \leq 2x + 9 \quad \text{and} \quad 2x + 9 < 1
\]
3. Solve the first inequality:
\[
-2 - 9 \leq 2x
\]
\[
-11 \leq 2x \implies x \geq -\frac{11}{2} = -5.5
\]
4. Solve the second inequality:
\[
2x + 9 < 1 \implies 2x < 1 - 9 \implies 2x < -8
\]
\[
x < -4
\]
5. Combine the results:
\[
-5.5 \leq x < -4
\]
The closest set from the options reflecting this inequality is **{x: -5.5 ≤ x < -4}**, however, it seems it isn't listed. The correct option should be checked according to the available responses.
### Question 3
**Inequality:** \( -12g + 18 > -5g + 53 \)
1. Rearrange the inequality:
\[
-12g + 5g > 53 - 18
\]
\[
-7g > 35
\]
2. Divide by \(-7\) (reverse the inequality):
\[
g < -5
\]
The solution is **g < -5**.
### Question 4
**Graph:** \( x \leq -3 \)
To graph this inequality, you would draw a number line, place a closed dot (since -3 is included) on -3, and shade to the left to indicate all values less than or equal to -3.
### Question 5
1. Solve \( 4x - 3 > 9 \):
\[
4x > 12 \implies x > 3
\]
2. Solve \( x + 6 > -2 \):
\[
x > -8
\]
The solution set is the intersection of the two results, which is \( x > 3 \).
Thus, the response should be **{x | x > 3}**.
### Question 6
Based on the given options and graphs, if the graph indicates values where \(x \leq -3\) or \(x > 1\), then the appropriate choice would be **\(x \leq -3\) or \(x > 1\)**.
### Question 7
**Inequality:** \( 25m - 7 \leq 17 \)
1. Add \(7\) to both sides:
\[
25m \leq 24
\]
2. Divide by \(25\):
\[
m \leq \frac{24}{25}
\]
So the solution to the inequality is **\( m \leq \frac{24}{25} \)**, which can be expressed as \( m \leq 0.96 \).
If you need any more clarification or specific formatting for responses, let me know!