Final answer:
The value of x is determined by the conditions that 2x - 1 must be less than or equal to 7 and 3x must be greater than or equal to 7. Solving these inequalities, we find that the possible range for x is 2.33 to 4.
Step-by-step explanation:
We need to find the value of x when the numbers 2, 2x - 1, 9, 3x, 15, 4x + 2, 22 are in ascending order, and the first quartile (Q1) of the data is 7.
The first quartile (Q1) is the median of the lower half of the data. Here, 7 numbers are given which means the lower half will contain the first three numbers once they are arranged in ascending order. Since the first quartile is 7, which is also one of our given numbers, it implies that 7 is the third number in the sequence when arranged in ascending order. Hence, the second number 2x - 1 must be less than or equal to 7. At the same time, the fourth number, 3x, must be greater than or equal to 7.
Given that, 2x - 1 ≤ 7 and 3x ≥ 7, we can solve for x.
- Add 1 to both sides of 2x - 1 ≤ 7: 2x ≤ 8
- Divide both sides by 2: x ≤ 4
- Divide both sides of 3x ≥ 7 by 3: x ≥ 7/3 or approximately x ≥ 2.33
Therefore, we can conclude that 2.33 ≤ x ≤ 4, which is the range for the value of x based on the provided quartile information.