Hi, Annie.

I'm guessing that the brackets really should be straight lines, to indicate absolute value?

An easy way to figure out this problem is to try it with a few heights that don't work, such as 25 and 55. The first 3 choices all yield true statements, so they do not support the regulation.

Looking closer at D & E, you can see that D is taking the median of 30 and 50 and comparing whether the child's height is less than 10 away from it.  Choice E is comparing whether that height is less than 5 away from 45; any height between 30 and 40 inclusive would not yield a true statement either, which doesn't satisfy our requirement.

D is your answer.

Hope this explanation helps you.

I assume that the brackets [] represent absolute values.

We can show the height of children that are allowed to ride the ride by the inequalities 30 < h and h < 50.

We can find the average height of children that are allowed to ride by adding the extremes and dividing by 2 (mid-point formula).

(50 + 30)/2

80/2

40

We can also find the number of inches from the midpoint to the extremes by subtracting the minimum from the maximum and divinding by 2.

(50 - 30)/2

20/2

10

Absolute value inequalities are set up as:

[vaiable (h) - mid-point of accepted range (40)] < or > distance from mid-point to extreme (10)

The answer is d, [h - 40] < 10.

First, you need to find the middle point of 30 and 50, which is 40.

Second, find the largest distance from the middle point, which is 50-40 = 10

Put this relation in absolute inequality form: |h-40| < 10.

Answer: d