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# M30-21

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Intern
Joined: 08 Aug 2017
Posts: 32

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28 Feb 2018, 22:25
Hi Bunuel

I have a doubt.
I took the three conditions as:
1. x<5
2. -5<=x<=5
3. x>5

As a result for the second condition i got y Ranging from -10 to 10 (Total of 21 integers), so my overall total was 23 instead of 21. I am struggling with the "equal to" sign, how do we know in which condition we place the "equal to" sign? In few problems that I solved before, I thought it does not really matter, however in this problem, it seems it does matter. I need to clear my concept. Thanks in advance for your kind help.
Math Expert
Joined: 02 Sep 2009
Posts: 55271

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28 Feb 2018, 23:20
pantera07 wrote:
Hi Bunuel

I have a doubt.
I took the three conditions as:
1. x<5
2. -5<=x<=5
3. x>5

As a result for the second condition i got y Ranging from -10 to 10 (Total of 21 integers), so my overall total was 23 instead of 21. I am struggling with the "equal to" sign, how do we know in which condition we place the "equal to" sign? In few problems that I solved before, I thought it does not really matter, however in this problem, it seems it does matter. I need to clear my concept. Thanks in advance for your kind help.

You are right, it does not matter where you place = sign as long as it's there somewhere. The point is that since x could be both -5 and 5, you should include both these values in either of the ranges. You'll get the same answer no matter where you place = sign. For example:

1. x < 5 --> y = -10 --> one value.

2. -5 <= x <= 5 --> y = 2x --> -10 < (y = 2x) < 10 --> 19 values (from -9 to 9).

3. x > 5 --> y = 10 --> one value.

1 + 19 + 1 = 21.
_________________
Intern
Joined: 19 Nov 2012
Posts: 28

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26 Jun 2018, 09:47
Bunuel wrote:
You have the same ranges - it does not matter in which range you include = sign.

Hi Bunuel,

if range in which you include = doesn't matter, can you please show how this question would work out if I consider the three ranges as follows:
1> X < -5
2> $$-5 < = X < = 5$$
3> x >5

I get
-10 1 value
22 22 values
10 1 value
Totally 24 values.
Let's say even I subtract 10 and -10 from those 24 values to eliminate double counting, I get 20 +2 =22 but not 21.
So I'm not doing something correct.

Thanks.
Intern
Joined: 10 Jul 2017
Posts: 30
Schools: ISB '20

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19 Aug 2018, 05:49
Dear Bunuel,
I did like this:
1) x>=5 ---> 1 integer (10)
2) x<=-5---> 1 integer (-10)
3) -5<x<5 ---- In this case I placed x=-4 and +4 in the expression, resulting in -8=< x =<8 ---> 17 integers
Therefore total no. of integers= 17+2 = 19
what am i doing wrong here?
Intern
Joined: 14 Jun 2018
Posts: 47
Location: India

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12 Oct 2018, 04:33
Bunuel wrote:
rsamant wrote:
when -5<x< 5

Why do you multiply I X-5 I by -1 ? ? I am trying to understand the logic behind this calculation
When -5<x<5, then |x+5|=x+5 and |x-5|=-(x-5)=5-x.

Absolute value properties:

When $$x \le 0$$ then $$|x|=-x$$, or more generally when $$\text{some expression} \le 0$$ then $$|\text{some expression}| = -(\text{some expression})$$. For example: $$|-5|=5=-(-5)$$;

When $$x \ge 0$$ then $$|x|=x$$, or more generally when $$\text{some expression} \ge 0$$ then $$|\text{some expression}| = \text{some expression}$$. For example: $$|5|=5$$.

Therefore, when -5 < x < 5, then x + 5 > 0 and x - 5 < 0, thus |x + 5| = x + 5 and |x - 5| = -(x - 5) = 5 - x.

Hope it helps.

Hello Bunuel,

Can you please share some similar OG questions? Link or any tags?
thank you!
Math Expert
Joined: 02 Sep 2009
Posts: 55271

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12 Oct 2018, 05:15
Shri15kumar wrote:
Bunuel wrote:
rsamant wrote:
when -5<x< 5

Why do you multiply I X-5 I by -1 ? ? I am trying to understand the logic behind this calculation
When -5<x<5, then |x+5|=x+5 and |x-5|=-(x-5)=5-x.

Absolute value properties:

When $$x \le 0$$ then $$|x|=-x$$, or more generally when $$\text{some expression} \le 0$$ then $$|\text{some expression}| = -(\text{some expression})$$. For example: $$|-5|=5=-(-5)$$;

When $$x \ge 0$$ then $$|x|=x$$, or more generally when $$\text{some expression} \ge 0$$ then $$|\text{some expression}| = \text{some expression}$$. For example: $$|5|=5$$.

Therefore, when -5 < x < 5, then x + 5 > 0 and x - 5 < 0, thus |x + 5| = x + 5 and |x - 5| = -(x - 5) = 5 - x.

Hope it helps.

Hello Bunuel,

Can you please share some similar OG questions? Link or any tags?
thank you!

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Re: M30-21   [#permalink] 12 Oct 2018, 05:15

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# M30-21

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