Here are the solutions for each question:
Question 1: Choose the correct solution for \( x + 12 \geq 5 \).
The inequality can be solved as follows: \[ x + 12 \geq 5 \] Subtracting 12 from both sides: \[ x \geq 5 - 12 \] \[ x \geq -7 \]
Correct Responses: \( x \geq -7 \) or \( x \) is greater than or equal to -7.
Question 2: Choose the correct solution for \( x + 3 < 12 \).
Solving: \[ x + 3 < 12 \] Subtracting 3 from both sides: \[ x < 12 - 3 \] \[ x < 9 \]
Correct Responses: None of the responses are correct here. If the response options included \( x < 9 \), it would be correct.
Question 3: Choose the correct solution for \( 6x < 14 \).
Solving: \[ 6x < 14 \] Dividing both sides by 6: \[ x < \frac{14}{6} \] \[ x < \frac{7}{3} \approx 2.33 \]
Correct Responses: \( x < 2.3 \)
Question 4: A graph of the inequality \( x < 3 \) would have a(n) circle at 3 and an arrow going to the left.
Question 5: Choose the correct solution for \( 5x - 11 \leq 14 \).
Solving: \[ 5x - 11 \leq 14 \] Adding 11 to both sides: \[ 5x \leq 25 \] Dividing by 5: \[ x \leq 5 \]
Correct Responses: \( x \leq 5 \) or \( x \) is less than or equal to 5.
Question 6: Choose the correct solution for \( 6.2x \geq 55.8 \).
Solving: \[ 6.2x \geq 55.8 \] Dividing both sides by 6.2: \[ x \geq \frac{55.8}{6.2} \approx 9 \]
Correct Responses: \( x \geq 9 \) or \( x \) is greater than or equal to 9.
Question 7: A graph showing the inequality \( x \geq -6 \) would have a(n) circle at -6 and an arrow going to the right.
Question 8: Twelve less than eight times a number is more than 52. What are all the possible values of the number?
The inequality to express this situation is: \[ 8x - 12 > 52 \]
Correct Responses: \( 8x - 12 > 52 \)
Question 9: A graph showing the inequality \( 7x < 49 \) would have a(n) circle at 7 and an arrow going to the left.
Question 10: Choose the correct solution for \( x + 16 < 4 \).
Solving: \[ x + 16 < 4 \] Subtracting 16 from both sides: \[ x < 4 - 16 \] \[ x < -12 \]
Correct Responses: \( x < -12 \).
If you have further questions or need additional assistance, feel free to ask!