The heights, h, of the students in the chorus at Central Middle School
satisfy the inequality
|h-57.5/2|¡Ü 3.25
when h is measured in inches.
Determine the interval in which these heights lie and express your
answer to the nearest tenth of a foot. [Only an algebraic solution can
receive full credit.]
before the 3.25 it's supposed to be a "less than or equal" to symbol.
( < or = )
555555555555555555
To determine the interval in which the heights of the students lie, we need to solve the given inequality:
|h - 57.5/2| ≤ 3.25
Step 1: Simplify the expression inside the absolute value:
h - 57.5/2 ≤ 3.25 and -(h - 57.5/2) ≤ 3.25
Step 2: Solve the two inequalities separately:
h - 57.5/2 ≤ 3.25 and -h + 57.5/2 ≤ 3.25
Step 3: Solve for h in each inequality:
h ≤ 3.25 + 57.5/2 and -h ≤ 3.25 - 57.5/2
Step 4: Simplify the expressions:
h ≤ 3.25 + 28.75 and -h ≤ 3.25 - 28.75
Step 5: Solve for h:
h ≤ 31 and -h ≤ -25.5
Step 6: Multiply the second inequality by -1 (which reverses the inequality):
h ≤ 31 and h ≥ 25.5
Step 7: Combine the two inequalities to form the interval solution:
25.5 ≤ h ≤ 31
Finally, we need to express the answer to the nearest tenth of a foot. Since there are 12 inches in a foot, we divide the interval endpoints by 12:
25.5/12 ≤ h ≤ 31/12
2.125 ≤ h ≤ 2.583333
Thus, the interval in which the heights of the students lie, expressed to the nearest tenth of a foot, is approximately 2.1 feet to 2.6 feet.