Math Destroyer Question

[xoNavidox]

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This question is from the 2010 version of Math Destroyer. It's Test 2 Question 40

What is the largest possible value of x in the expression |16-2x| ≤ 4?
A. 4
B. 6
C. 8
D. 10
E. no limit

The answer is 10.

Since it's absolute value it can be both |16-2x| ≤ 4 and |2x-16| ≤ 4, which is also what it says in the back of the book. When I do the problem out, I get x≥6 for |16-2x| ≤ 4 and x≤10 for |2x-16| ≤ 4. Since it's asking for the largest possible value of x, wouldn't the answer be infinity (no limit) because x is larger than 6?

I feel like there's something really obvious I'm not seeing 😕

 

[ushaseos]

Well think of it like so |4| ≤ 4 and |-4| ≤ 4

How can we generate -4 in the absolute value?
16-2x = -4
-2x = -20
x=10

Mathematically it boils down to

16 - 2x ≤ 4 or - (16 - 2x) ≥ 4

EDIT - the absolute value hides 2 inequalities. One where you just remove the absolute value. The other where you change the absolute value into parenthesis, put a minus sign before the parenthesis and change the sign of the inequality.

 

[NDPitch]

EDIT - the absolute value hides 2 inequalities. One where you just remove the absolute value. The other where you change the absolute value into parenthesis, put a minus sign before the parenthesis and change the sign of the inequality.

This is super information. Inequalities with absolute values have been throwing me for a loop recently.

 

[xoNavidox]

Thanks! That was really helpful!

 

[Dgeorg6]

The fastest way to do this problem is to simply plug in the largest # that is given and see if it works (which it does). If you are given a choice such as no limit, you can see that since 10 was exactly 4 it is not possible for it to be any higher, but if you dont just plug in the next biggest thing (in this case 11) and see if it works, and it doesn't.

This way you can just do simple math in your head without writing anything down.

 

[ushaseos]

The fastest way to do this problem is to simply plug in the largest # that is given and see if it works (which it does). If you are given a choice such as no limit, you can see that since 10 was exactly 4 it is not possible for it to be any higher, but if you dont just plug in the next biggest thing (in this case 11) and see if it works, and it doesn't.

This way you can just do simple math in your head without writing anything down.

Absolutely true. When in doubt plug and chug. I just wanted to let you guys know the math behind it, but Dgeog6 is offering the better test taking tip.

Good luck you guys!