Which compound sentence has its solution set shown on the graph below? -1 1 2 4 6. 7 2 x- 4 > 6 or 3 x<9 3 x+ 8 <-7 and -4 x> 12 2 x- 4 < 6 and 3 x> 9 3 x+ 8 > -7 or -4 x< 12
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#15
![**Which compound sentence has its solution set shown on the graph below?**
[Graph Description]
The graph is a number line that ranges from -1 to 7. There are open circles at the points 3 and 5, with a solid line connecting these two points. This indicates that the solution set includes all values between 3 and 5, but not the values of 3 and 5 themselves (i.e., 3 < x < 5).
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- ○ \( 2x - 4 > 6 \) **or** \( 3x < 9 \)
- ○ \( 3x + 8 < -7 \) **and** \( -4x > 12 \)
- ○ \( 2x - 4 < 6 \) **and** \( 3x > 9 \)
- ○ \( 3x + 8 > -7 \) **or** \( -4x < 12 \)
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**Explanation:**
To determine which compound sentence represents the graphed solution, we need to evaluate which inequality matches the range 3 < x < 5.
- The first option, \( 2x - 4 > 6 \) or \( 3x < 9 \), simplifies to \( x > 5 \) or \( x < 3 \), which does not match the graph (values outside 3 and 5).
- The second option, \( 3x + 8 < -7 \) and \( -4x > 12 \), results in no solution for x when simplified.
- The third option, \( 2x - 4 < 6 \) and \( 3x > 9 \), simplifies to \( x < 5 \) and \( x > 3 \), which matches the graph (values between 3 and 5). Hence, this is the correct choice.
- The fourth option, \( 3x + 8 > -7 \) or \( -4x < 12 \), simplifies to \( x > -5 \) or \( x > -3 \), which represents all real numbers and does not match the graph.
Thus, the correct answer is:
- ○ \( 2x - 4 < 6 \) **and** \( 3x > 9 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbc025c59-6bdc-48be-a1f1-041a40d15255%2F42983ead-45f8-49ac-af02-da14bb59098e%2Fy2nyy5u_processed.png&w=3840&q=75)
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