Question
Question 1 A)Determine the solution set of 2x>−8 and −5x+7=122x>−8 and −5x+7=12(1 point) Responses {−1}{−1}start set negative 1 end set {−4}{−4}start set negative 4 end set {x|x>−4}{x|x>−4}start set x such that x is greater than negative 4 end set {x|x>−1}{x|x>−1}start set x such that x is greater than negative 1 end set Question 2 A)Determine the solution set of −3x+7=10 or 3x−9=0−3x+7=10 or 3x−9=0(1 point) Responses {−1}{−1}start set negative 1 end set {−1,3}{−1,3}start set negative 1 comma 3 end set The solution set is null The solution set is null {3}{3}start set 3 end set
Answers
GPT-4o mini
Let's solve the questions step by step.
### Question 1:
We have two inequalities:
1. \( 2x > -8 \)
2. \( -5x + 7 = 12 \)
**Step 1: Solve the inequality \( 2x > -8 \)**
To isolate \( x \), we divide both sides by 2:
\[
x > -4
\]
**Step 2: Solve the equation \( -5x + 7 = 12 \)**
Rearranging the equation gives:
\[
-5x = 12 - 7 \\
-5x = 5 \\
x = -1
\]
### Solution for Question 1:
- The solution set for the inequality \( 2x > -8 \) is \( \{ x | x > -4 \} \).
- The solution for the equation \( -5x + 7 = 12 \) gives \( x = -1 \).
### Final answer for Question 1:
The correct responses from the options presented in the question clearly match:
\{x | x > -4\}
---
### Question 2:
We have two equations:
1. \( -3x + 7 = 10 \)
2. \( 3x - 9 = 0 \)
**Step 1: Solve the equation \( -3x + 7 = 10 \)**
Rearranging gives:
\[
-3x = 10 - 7 \\
-3x = 3 \\
x = -1
\]
**Step 2: Solve the equation \( 3x - 9 = 0 \)**
Rearranging gives:
\[
3x = 9 \\
x = 3
\]
### Solution for Question 2:
- The solution set we found is \( x = -1 \) and \( x = 3 \).
### Final answer for Question 2:
The correct response would be:
\{−1, 3\}
---
In summary, the answers are:
- **Question 1:** \{x | x > -4\}
- **Question 2:** \{-1, 3\}
### Question 1:
We have two inequalities:
1. \( 2x > -8 \)
2. \( -5x + 7 = 12 \)
**Step 1: Solve the inequality \( 2x > -8 \)**
To isolate \( x \), we divide both sides by 2:
\[
x > -4
\]
**Step 2: Solve the equation \( -5x + 7 = 12 \)**
Rearranging the equation gives:
\[
-5x = 12 - 7 \\
-5x = 5 \\
x = -1
\]
### Solution for Question 1:
- The solution set for the inequality \( 2x > -8 \) is \( \{ x | x > -4 \} \).
- The solution for the equation \( -5x + 7 = 12 \) gives \( x = -1 \).
### Final answer for Question 1:
The correct responses from the options presented in the question clearly match:
\{x | x > -4\}
---
### Question 2:
We have two equations:
1. \( -3x + 7 = 10 \)
2. \( 3x - 9 = 0 \)
**Step 1: Solve the equation \( -3x + 7 = 10 \)**
Rearranging gives:
\[
-3x = 10 - 7 \\
-3x = 3 \\
x = -1
\]
**Step 2: Solve the equation \( 3x - 9 = 0 \)**
Rearranging gives:
\[
3x = 9 \\
x = 3
\]
### Solution for Question 2:
- The solution set we found is \( x = -1 \) and \( x = 3 \).
### Final answer for Question 2:
The correct response would be:
\{−1, 3\}
---
In summary, the answers are:
- **Question 1:** \{x | x > -4\}
- **Question 2:** \{-1, 3\}
Use the image to answer the question. Select the solution set represented on the graph (1 point) Responses x≥−8 and x≤−2x≥−8 and x≤−2x≥−8 and x≤−2x≥−8 and x≤−2 x>−8 and x<−2x>−8 and x<−2x>−8 and x<−2x>−8 and x<−2 x>−8 or x<−2x>−8 or x<−2x>−8 or x<−2x>−8 or x<−2 x≥−8 or x≤−2
GPT-4o mini
To answer your question accurately based on the graph you referenced, I need a description or details about the graph since I cannot see images. However, I can help you understand how to analyze a graph to identify solution sets.
### Steps to Determine the Solution Set from a Graph:
1. **Identify the Axes:** Look for the x-axis and the bounds depicted on it.
2. **Check the Shading:** Determine how the region is shaded:
- **Solid Lines vs. Dotted Lines:** A solid line typically indicates that the endpoint is included (≥ or ≤), while a dotted line indicates it is not included (> or <).
- **Direction of Shading:** If the shading goes to the right, it typically represents "greater than" (>) or "greater than or equal to" (≥); if it goes to the left, it represents "less than" (<) or "less than or equal to" (≤).
3. **Check Intersection Points:** Look for critical points (like -8 and -2 mentioned in your options). Identify if these points are included in the shading or excluded.
**Final Analysis:**
- If the graph shows an area from \( -8 \) to \( -2 \) inclusively, it would correspond to the solution \( x ≥ -8 \) and \( x ≤ -2 \).
- If it has open ends (without solid lines at \( -8 \) or \( -2\)), then it could correspond to \( x > -8 \) and \( x < -2 \).
If you can provide a description of the graph or the parameters displayed (such as the color or type of line), I can help you select the correct response from your options.
### Steps to Determine the Solution Set from a Graph:
1. **Identify the Axes:** Look for the x-axis and the bounds depicted on it.
2. **Check the Shading:** Determine how the region is shaded:
- **Solid Lines vs. Dotted Lines:** A solid line typically indicates that the endpoint is included (≥ or ≤), while a dotted line indicates it is not included (> or <).
- **Direction of Shading:** If the shading goes to the right, it typically represents "greater than" (>) or "greater than or equal to" (≥); if it goes to the left, it represents "less than" (<) or "less than or equal to" (≤).
3. **Check Intersection Points:** Look for critical points (like -8 and -2 mentioned in your options). Identify if these points are included in the shading or excluded.
**Final Analysis:**
- If the graph shows an area from \( -8 \) to \( -2 \) inclusively, it would correspond to the solution \( x ≥ -8 \) and \( x ≤ -2 \).
- If it has open ends (without solid lines at \( -8 \) or \( -2\)), then it could correspond to \( x > -8 \) and \( x < -2 \).
If you can provide a description of the graph or the parameters displayed (such as the color or type of line), I can help you select the correct response from your options.