Which one of the following intervals is not symmetric about x=...

Question

Which one of the following intervals is not symmetric about x=5?

a.(1, 9)

b.(4, 6)

c.(3, 8)

d.(4.5, 5.5)

Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says to identify the interval that is not symmetric about X equal to -3, and we're given 4 possible choices as our answers. For choice A, we have the open interval from -6 to 0. For choice B, we have the open interval from -4 to -2. For choice C, we have the open interval from -5 to -1. And for choice D, we have none of these. Now we need to determine which of our intervals is not symmetric about X equal to -3. Now, if an interval is symmetric about X equal to -3, then its midpoint is going to be -3. So we need to do is calculate the midpoint of each of the intervals in choices A, B, and C. So we're gonna start off with the interval of the open interval from -6 to 0, and calculate its midpoint. So, we'll label that midpoint as X. And recall to calculate the midpoint, we just need to add together the two endpoints and then divide by 2. So X is going to be equal to the quantity of minus 6 plus 0 in quantity divided by 2. And when we simplify this, this is going to be equal to -3. So that means that the first interval, the open interval from -6 to 0, is symmetric about X equal to -3, since its midpoint is equal to -3. So we'll look at the next interval, which is the open interval from -4 to -2. And again, Warren calculate the midpoint the same way. We'll have X is equal to. The quantity of -4 + -2. In quantity divided by 2. And again, when we simplify this, this is going to be equal to -3. So again, the midpoint of this interval is -3, so this interval is symmetric about X equal to -3. And then finally for our last interval, that's gonna be the open interval from -5 to -1. And again, we're gonna calculate the midpoint, so we'll have X is equal to the quantity of -5 plus -1. In quantity, divided by 2, and again, this is equal to minus 3 when we simplify that expression. So again, this interval is symmetric about X equal to -3 since its midpoint is equal to -3. So, we have the midpoint of -3 for all three intervals. So all three intervals are symmetric about X equal to -3. So that means that none of these intervals are not symmetric about X equal to -3. So the correct answer for this um problem is D, none of these. So I hope that this explanation has been useful, and I'll see you in the next video.

Which one of the following intervals is not symmetric about x=5?
a.(1, 9)
b.(4, 6)
c.(3, 8)
d.(4.5, 5.5)

Key Concepts

Symmetry in Intervals

Endpoints of an Interval

Calculating Midpoints

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