Absolute Value Inequalities

O

Old Man

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Jan 31, 2011
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Hello board. My son has a few problems on his homework that are beyond my recollection. I consider myself sufficient enough at math, that given an answer, I can usually work the solution in reverse. However, his teacher only assigns the even problems (odds answers are supplied in the back of the book). Any help would be greatly appreciated. The two word problems are:

Spring Oscillation: A weight attached to a spring hangs at rest, a distance of x inches off of the ground. If the weight is pulled down a distance of l inches and released, the weight begins to bounce and it's distance is d inches off of the ground. If the distance the spring is off the ground is 4 feet and the spring is pulled down 3 inches and released:
A. Write the absolute value inequality that models the situation.
B. Find what distances from the ground the weight will oscillate between

Submarine Depth: The sonar operator on a submarine detects an old World War II submarine net and must decide to detour over or under the net. The computer gives the operator a depth model of |d-394|-20>164, where d is the depth in feet that represents safe passage. At what depths should the submarine travel to avoid the net?
 
Old Man said:
Hello board. My son has a few problems on his homework that are beyond my recollection. I consider myself sufficient enough at math, that given an answer, I can usually work the solution in reverse. However, his teacher only assigns the even problems (odds answers are supplied in the back of the book). Any help would be greatly appreciated. The two word problems are:

Spring Oscillation: A weight attached to a spring hangs at rest, a distance of x inches off of the ground. If the weight is pulled down a distance of l inches (measured from where? from the rest position? from the ground?) and released, the weight begins to bounce and it's distance is d inches off of the ground. If the distance the spring is off the ground is 4 feet and the spring is pulled down 3 inches and released:

A. Write the absolute value inequality that models the situation.
B. Find what distances from the ground the weight will oscillate between


Assuming that the distance 'l' is measured off the ground:

A. |x-d| ? x - l

Now continue.....


Submarine Depth: The sonar operator on a submarine detects an old World War II submarine net and must decide to detour over or under the net. The computer gives the operator a depth model of |d-394|-20>164, where d is the depth in feet that represents safe passage. At what depths should the submarine travel to avoid the net?
Click to expand...

Why isn't your son asking for help here - showing the work he has done?
 
I assume l is measured from the ground. So, pulled down 3 inches would put the weight at a height of 3'9" from the ground. I realize the problem is poorly written. I had made spelling/grammar corrections from my son's paper as I went. I was actually a little disappointed until I went to find the problem in the book. Turns out this was on a hand out from the teacher, that he copied verbatim. Now I am disappointed in the teacher, but I digress.

My son came to me for help as he always does. My first thought wasn't to send him to the internet because I did not know. I asked him to leave it, and I would go over it. I would rather be able to relearn it myself, and then show him how to solve it in terms that I know he will understand. I appreciate any and all help I might find here. I was scouring the internet for models on absolute value inequalities, and came across this forum. Everything I have come across models how to solve these problems with supplied inequalities, not how to construct the inequality yourself.
 
I never did figure out the first problem. If I use your supplied inequality, and plug in the numbers, |x-d| ? x - l
Converting feet to inches.
|48-d| ? 48 - 3
|48-d| ? 45
-45 ? 48-d ? 45
-93 ? -d ? -3
-92 ? d ? -2

Maybe I did this wrong, but I do not believe so. How can the weight oscillate between negative numbers or distances below the ground/0?
 
Old Man said:
I never did figure out the first problem. If I use your supplied inequality, and plug in the numbers, |x-d| ? x - l
Converting feet to inches.
|48-d| ? 48 - 3
|48-d| ? 45
-45 ? 48-d ? 45
-93 ? -d ? -3

93 >= d >= 3


-92 ? d ? -2

Maybe I did this wrong, but I do not believe so. How can the weight oscillate between negative numbers or distances below the ground/0?
Click to expand...
 
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