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## #1 2022-04-03 08:57:24

Member
Registered: 2021-02-20
Posts: 44

### Absolute value inequality

Hello,

Is my answer correct?

3. Mark is cutting fence posts that are 48 inches tall to sell. He is permitted a 2 inch margin of error. Otherwise, he cannot sell the fence posts. What absolute value inequality models this situation?

A. |x - 48| ≤ 2
B. |x + 48| ≤ 2
C. |x - 2| ≤ 48
D. |x + 2| ≤ 48

The right one is alternative A.

Thank you,

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## #2 2022-04-03 09:17:21

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,425
Website

### Re: Absolute value inequality

Yes, that's right.

One way you can check your answer is just to consider some different fence post heights. Suppose you had a fence post that was 49 inches tall -- this is clearly within the 2 inch margin of error. According to the inequality in option A, we have:

|x - 48| = |49 - 48| = 1

and this is less than or equal to 2, so the inequality works in this case.

Similarly if you choose a fence post height of 47 inches, your inequality will still hold.

If you had a fence post of 51 inches then your inequality shouldn't hold -- and indeed in this case we have |x - 48| = |51 - 48| = 3, which is not less than or equal to 2. So your inequality correctly distinguishes between fence posts within a 2 inch margin of error and those that aren't.

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## #3 2022-04-03 09:25:15

Member
Registered: 2021-02-20
Posts: 44

### Re: Absolute value inequality

I am having trouble with this exercise.

4. Which is a factor of  8x^2 + 4x - 24 when it is completely factored?

A. (2x + 3)
B. (x - 2)
C. (x + 2)
D. (x + 3)

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## #4 2022-04-03 13:44:26

Jai Ganesh
Registered: 2005-06-28
Posts: 44,438

### Re: Absolute value inequality

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #5 2022-04-03 20:18:47

Bob
Registered: 2010-06-20
Posts: 9,864

### Re: Absolute value inequality

Set a possible factor equal to zero and find x; now try that value of x in the quadratic . If that evaluates to zero you've got a factor.

2x + 3 = 0 means x = -1.5

so this is not the factor.

If x + 2 = 0 then x = -2

so this one is a factor.

This technique uses something called the factor theorem.

You'll find it half way down this page: https://www.mathsisfun.com/algebra/poly … actor.html

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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## #6 2022-06-10 01:40:09

Hicies87
Member
From: Portsmouth
Registered: 2022-01-22
Posts: 15

ganesh wrote:

thanks

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## #7 2022-06-12 09:12:05

Hicies87
Member
From: Portsmouth
Registered: 2022-01-22
Posts: 15

ganesh wrote: