The heights h of two-thirds of the members of a population satisfy the inequality |h-68.5/2.7|≤1 where h is measured in inches.Determine the interval on the real number line in which these heights lie.
assuming parentheses to make it
|(h-68.5)/2.7|≤1
(otherwise there'd be no reason to have a numeric fraction, as written)
|h-68.5| <= 2.7
so, h is within 2.7 of 68.5, and
65.8 <= h <= 71.2
I solved it already but thanks for the great help! It just confirmed my answer.:)
Why didn't use the two third value
Why didn't use the two third value of h in this problem
In this problem what is the meaning of two thirds of members
To determine the interval on the real number line in which these heights lie, we need to consider the inequality given: |h - 68.5/2.7| ≤ 1.
First, let's simplify the inequality:
|h - 68.5/2.7| ≤ 1
We can start by multiplying both sides by 2.7 to eliminate the fraction:
2.7|h - 68.5/2.7| ≤ 2.7
Next, divide both sides by 2.7 to isolate the absolute value expression:
|h - 68.5/2.7| ≤ 1/2.7
Simplifying even further, we get:
|h - 25.37| ≤ 0.37
Now, we will consider two cases for the absolute value expression.
Case 1: h - 25.37 ≥ 0
In this case, the inequality becomes:
h - 25.37 ≤ 0.37
Solving for h:
h ≤ 0.37 + 25.37
h ≤ 25.74
Case 2: h - 25.37 < 0
In this case, the inequality becomes:
-(h - 25.37) ≤ 0.37
Solving for h:
h - 25.37 ≥ -0.37
h ≥ -0.37 + 25.37
h ≥ 25
Therefore, the heights lie within the closed interval [25, 25.74] on the real number line.