Final answer:
The number line representing the solution 1.5 ≤ x ≤ 4.5 corresponds to the inequality d) -3x - 15 ≤ -27, which indicates that the value of x is any number greater than or equal to 4, including the part of the range from 4 to 4.5.
Step-by-step explanation:
The number line given in the question is said to represent the solution to an inequality. The solution is shown as 1.5 ≤ x ≤ 4.5, which means the value of x is within the range of 1.5 and 4.5 inclusive. Therefore, we'll check which of the given inequalities corresponds to this solution when we solve them.
- Solving inequality a) -2x + 7 < 28 would give us x > -10.5, which does not match our range.
- For inequality b) 6x - 9 ≥ -21, solving it yields x ≥ 2, which is too broad as it includes numbers greater than 4.5.
- Inequality c) 7x + 11 > 54 simplifies to x > 6.14, which again, does not fit within our scope.
- Finally, the inequality d) -3x - 15 ≤ -27 simplifies to x ≥ 4. This inequality indicates that the value of x is any number greater than or equal to 4, matching our range from 4 to 4.5 from the given number line.
Thus, the correct inequality represented by the number line 1.5 ≤ x ≤ 4.5 is d) -3x - 15 ≤ -27.