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A regulation for riding a certain amusement park ride requires that a child be between 30 inches and 50 inches tall. Which of the following inequalities can be used to determine whether or not a child's height (h) satisfies the regulation for this ride?

a) [h-10]<50

b) [h-20]<40

c) [h-30]<20

d) [h-40]<10

e) [h-45]<5

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.

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.