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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

3 answers

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}
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

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.