Final answer:
The inequality 3/2 x - 2 ≥ 5 1/2 represents that x is greater than or equal to 5. This is shown as a closed circle at 5 on a number line, with a line extending to the right to indicate all values of x that satisfy the inequality.
Step-by-step explanation:
To determine what the inequality 3/2 x - 2 ≥ 5 1/2 represents on a number line, we first solve for x. Convert the mixed number to an improper fraction: 5 1/2 is equal to 11/2. We then have the inequality: 3/2 x - 2 ≥ 11/2.
Add 2 to both sides of the inequality to isolate the term with x:
3/2 x ≥ 11/2 + 2 which simplifies to 3/2 x ≥ 15/2. Now, multiply both sides by the reciprocal of 3/2 (which is 2/3) to solve for x:
x ≥ (15/2) × (2/3) which simplifies to x ≥ 5. Therefore, the inequality represents all values of x greater than or equal to 5, which is option (a).
On a number line, this would be indicated by a closed circle at 5 and a line extending to the right, showing all the numbers greater than or equal to 5.