The heights, h of the students in the chorus at Central Middle School satisfy the inequality absolute value of h-57.5/2< or = 3.25. Determine the interval in which these heights lie.
To determine the interval in which the heights of the students lie, we need to solve the inequality:
| (h - 57.5) / 2 | ≤ 3.25
Let's break down the steps to solve this inequality:
Step 1: Remove the absolute value by considering both cases:
Case 1: (h - 57.5) / 2 ≤ 3.25
Case 2: -((h - 57.5) / 2) ≤ 3.25
Step 2: Solve for h in each case:
Case 1: (h - 57.5) / 2 ≤ 3.25
Multiply both sides by 2:
h - 57.5 ≤ 6.5
Add 57.5 to both sides:
h ≤ 64
Case 2: -((h - 57.5) / 2) ≤ 3.25
Multiply both sides by -2 (this flips the inequality):
h - 57.5 ≥ -6.5
Add 57.5 to both sides:
h ≥ 51
Step 3: Combine the solutions from both cases:
The solution for h in case 1 is h ≤ 64, and in case 2 is h ≥ 51. To find the interval in which these heights lie, we look for the intersection between both cases.
Therefore, the heights h of the students in the chorus at Central Middle School lie in the interval [51, 64].