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# What is the value of |x+4|+x?

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Manager
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What is the value of |x+4|+x?  [#permalink]

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09 Dec 2014, 06:15
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Question Stats:

45% (01:28) correct 55% (01:19) wrong based on 220 sessions

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What is the value of |x+4|+x?

(1) x ≤ −4

(2) |x+4| = 0

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aimtoteach

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Re: What is the value of |x+4|+x?  [#permalink]

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09 Dec 2014, 06:19
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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: $$|5|=5$$.

What is the value of |x+4|+x?

(1) x ≤ −4 --> x + 4 ≤ 0, thus |x + 4| = -(x + 4). Therefore |x + 4| + x = -(x + 4) + x = -4. Sufficient.

(2) |x+4| = 0 --> x = -4 --> |x + 4| + x = 0 - 4 = -4. Sufficient.

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Re: What is the value of |x+4|+x?  [#permalink]

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10 Mar 2017, 00:16
1
St 1: x≤4. mod will open with negative sign. hence the expression will be -x-4+x =-4. ANSWER
St 2: |x+4| = 0 or x = -4. putting the value in expression we get |-4+4| - 4 = -4 ANSWER

option D
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Re: What is the value of |x+4|+x?  [#permalink]

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10 Mar 2017, 00:21
Bunuel wrote:
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: $$|5|=5$$.

What is the value of |x+4|+x?

(1) x ≤ −4 --> x + 4 ≤ 0, thus |x + 4| = -(x + 4). Therefore |x + 4| + x = -(x + 4) + x = -4. Sufficient.

(2) |x+4| = 0 --> x = -4 --> |x + 4| + x = 0 - 4 = -4. Sufficient.

Could you please explain the first statement.TIA.
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Re: What is the value of |x+4|+x?  [#permalink]

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10 Mar 2017, 02:39
Chemerical71 wrote:
Bunuel wrote:
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: $$|5|=5$$.

What is the value of |x+4|+x?

(1) x ≤ −4 --> x + 4 ≤ 0, thus |x + 4| = -(x + 4). Therefore |x + 4| + x = -(x + 4) + x = -4. Sufficient.

(2) |x+4| = 0 --> x = -4 --> |x + 4| + x = 0 - 4 = -4. Sufficient.

Could you please explain the first statement.TIA.

Since x + 4 ≤ 0, then |x + 4| = -(x + 4) (When $$x \le 0$$ then $$|x|=-x$$). There fore |x + 4| + x = -(x + 4) + x = -4.
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Re: What is the value of |x+4|+x?  [#permalink]

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10 Mar 2017, 23:01
Bunuel wrote:
Chemerical71 wrote:
Bunuel wrote:
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: $$|5|=5$$.

What is the value of |x+4|+x?

(1) x ≤ −4 --> x + 4 ≤ 0, thus |x + 4| = -(x + 4). Therefore |x + 4| + x = -(x + 4) + x = -4. Sufficient.

(2) |x+4| = 0 --> x = -4 --> |x + 4| + x = 0 - 4 = -4. Sufficient.

Could you please explain the first statement.TIA.

Since x + 4 ≤ 0, then |x + 4| = -(x + 4) (When $$x \le 0$$ then $$|x|=-x$$). There fore |x + 4| + x = -(x + 4) + x = -4.

I have read all the above explanations, but I still dont understand how can an absolute/modulus of any term equals its negative value. Imho |x|=x and |-x|=x. Could you please throw some light on this? May be I am interpreting it wrong.
I solved the statement 1 using test values viz. x=-4,-5,-6 .
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What is the value of |x+4|+x?  [#permalink]

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Updated on: 11 Mar 2017, 03:23
1

I have read all the above explanations, but I still dont understand how can an absolute/modulus of any term equals its negative value. Imho |x|=x and |-x|=x. Could you please throw some light on this? May be I am interpreting it wrong.
I solved the statement 1 using test values viz. x=-4,-5,-6 .

Definition of modulus:
For any real number $$x$$, modulus is defiend as follows:
$$|x| = \begin{cases} x, & \mbox{if } x \ge 0 \\ -x, & \mbox{if } x < 0. \end{cases}$$

To solve any modulus question first find the critical point(i.e. a value or point where sign changes).

In case of |x+4| critical point is -4. So we have following:

$$|x+4| = \begin{cases} x+4, & \mbox{if } x \ge -4 \\ -(x+4), & \mbox{if } x < -4. \end{cases}$$

Now you can check whether above expression satisfies the modulus property or not.

Consider x = -5 , in this case |x+4| = -(x+4) = -(-5+4) = 1 (a positive value)

x = -2 , in this case |x+4| = x+4 = -2+4 = 2 (again a positive value)

x = -4, |x+4| = x+4 = -4+4 = 0 (a non-negative value).

Hope it helps.

Originally posted by ganand on 11 Mar 2017, 00:31.
Last edited by ganand on 11 Mar 2017, 03:23, edited 1 time in total.
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Re: What is the value of |x+4|+x?  [#permalink]

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11 Mar 2017, 03:13
Bunuel wrote:
Chemerical71 wrote:
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: $$|5|=5$$.

What is the value of |x+4|+x?

(1) x ≤ −4 --> x + 4 ≤ 0, thus |x + 4| = -(x + 4). Therefore |x + 4| + x = -(x + 4) + x = -4. Sufficient.

(2) |x+4| = 0 --> x = -4 --> |x + 4| + x = 0 - 4 = -4. Sufficient.

Since x + 4 ≤ 0, then |x + 4| = -(x + 4) (When $$x \le 0$$ then $$|x|=-x$$). There fore |x + 4| + x = -(x + 4) + x = -4.

I have read all the above explanations, but I still dont understand how can an absolute/modulus of any term equals its negative value. Imho |x|=x and |-x|=x. Could you please throw some light on this? May be I am interpreting it wrong.
I solved the statement 1 using test values viz. x=-4,-5,-6 .

Have you read the highlighted part?

It seems that you should brush-up fundamentals on absolute values:

Hope it helps.
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Re: What is the value of |x+4|+x?  [#permalink]

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30 Jan 2019, 07:51
1
Here's how I solved it, feel free to critique!

What is the value of |x+4|+x?

Since anything in the mod has a value > 0, 'x' will be < -4.

Statement 1: x<-4
This matches what was already discussed and through testing a couple numbers, the result of the equation will always equal -4.
Sufficient

Statement 2: |x+4|=0
I went through and solved for both scenarios and found x=-4 for both. Since there is a unique value for x the equation can be solved for a unique answer.
Sufficient

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Re: What is the value of |x+4|+x?  [#permalink]

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30 Jan 2019, 09:15
1
aimtoteach wrote:
What is the value of |x+4|+x?

(1) x ≤ −4

(2) |x+4| = 0

(1) Let x = -4, then |-4+4| -4 = -4

Let x =-4.5 then |-4.5+4| =4.5 = .5-4.5 = -4

Let x =-10 Then |-10+4| -10 = |-6| -10 = 6-10 =-4

So you can see that no matter what value we test for x<=-4, we get -4 Suff

(2) |x+4| = 0, then x +4 = 0 and x= -4. Then |-4 +4| - 4 = -4 Suff

Re: What is the value of |x+4|+x?   [#permalink] 30 Jan 2019, 09:15
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