Math Destroyer Test 2 #40

[Mufasha]

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I'll preface this by saying I'm awful at math. The Math Destroyer is totally kicking my butt, but I'm learning from it. I am, however, confused on this question involving an absolute value inequality. The way I'm interpreting this, I thought E (no limit) would be the answer because the solution to 16 - 2x ≤ 4 would equal x ≥ 6 whereas the other solution would be x ≤ 10 (at least I think so!)

I'm sure I'm doing something wrong, but I can't figure out what. I've include the question, the solution, and my interpretation of it.

 

[CoFe2]

for questions like this on the DAT, my strategy is to plug and chug.
just put in the different numbers for x and see what happens.
when you put in 10 you get 16-20 which = -4 but the absolute value of that is 4 so it fits the equation because it is greater or equal to 4
next put in a number bigger than 10, like 11. 16-22=-6 which is actually 6 because of the absolute value. this does NOT fit in the equation because 6 is bigger than 4.

hope this helps!

 

[KyoPhan]

If it was no limit, we can try plugging in a really big number. Doing this will probably give you a mismatch.

You need to switch the sign at the very beginning for the bottom half, which should give you -16+2x>4.
Solving it will give you x<10.


If you take a simpler example such as |x|<2, by your method,
you'll get x<2 and -x>2

Solve the right, you get -x>2 ----> x>-2
Final ans: x<2 and x>-2 or 2>x>-2

And you can check the answer if you plug in a few numbers like -1, 1, -2, and so on. You won't really have time to do this, but just for sake of convincing yourself.

 

[Mufasha]

Thank you! I feel pretty silly now because E clearly doesn't work when you look at it. I was just focused on doing the math out and I didn't notice my answer made no logical sense. But I get it now, so thanks again!

 

[el_duderino]

Split into two equations:
16-2x <=4
16-2x >= -4