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What is the value of x? |x+2|+|x−3|=|2x+3|

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What is the value of x? |x+2|+|x−3|=|2x+3| [#permalink]

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New post 25 Oct 2017, 07:12
1
1
1
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

79% (01:24) correct 21% (00:59) wrong based on 217 sessions

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What is the value of x?
|x+2|+|x−3|=|2x+3|

A. -5
B. -2
C. 1
D. 4
E. 7
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Re: What is the value of x? |x+2|+|x−3|=|2x+3| [#permalink]

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New post 25 Oct 2017, 07:33
4
3
div10 wrote:
What is the value of x?
|x+2|+|x−3|=|2x+3|

A. -5
B. -2
C. 1
D. 4
E. 7


The ideal way to get the answer is by solving for different ranges of x. The above equation will take 4 different forms for the following ranges:
1. Greater than 3
2. From -1.5 to 3
3. From -2 to -1.5
4. Less than -2

Solving for each range separately, only one range gives a valid answer, which is 1.

A much easier way to solve this - substitute the options!

Hope this helps!




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What is the value of x? |x+2|+|x−3|=|2x+3| [#permalink]

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New post 25 Oct 2017, 10:10
1
2
div10 wrote:
What is the value of x?
|x+2|+|x−3|=|2x+3|

A. -5
B. -2
C. 1
D. 4
E. 7

Using the answer choices is the fastest.

If you do not know how to use critical values and intervals, see this post, below, with links to excellent material on complex absolute value questions.
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that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

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Re: What is the value of x? |x+2|+|x−3|=|2x+3| [#permalink]

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New post 26 Oct 2017, 12:56
If nothing strikes, just put all values one by one, you will get 1 will only satisfy.


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Re: What is the value of x? |x+2|+|x−3|=|2x+3| [#permalink]

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New post 06 Jan 2018, 12:47
@genxer123 Can you explain how you go 1 in case 4?? isn't

Case 4
|x+2|+|x−3|=|2x+3|

−x−2−x+3=−2x−3
-2x+1 = -2x-3
1=-3

which is invalid???
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Re: What is the value of x? |x+2|+|x−3|=|2x+3| [#permalink]

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New post 06 Jan 2018, 13:02
1
RashmiT wrote:
@genxer123 Can you explain how you go 1 in case 4?? isn't

Case 4
|x+2|+|x−3|=|2x+3|

−x−2−x+3=−2x−3
-2x+1 = -2x-3
1=-3

which is invalid???


Hi RashmiT

Yes you are correct in your observation. Case 4 by generis is incorrect.

This question is best solved through options. if you go for any other approach then you will have to work through multiple ranges.
Another option to remove mod is to square both sides but it will result in a complex polynomial equation.
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What is the value of x? |x+2|+|x−3|=|2x+3| [#permalink]

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New post 06 Jan 2018, 13:59
1
RashmiT wrote:
@genxer123 Can you explain how you go 1 in case 4?? isn't

Case 4
|x+2|+|x−3|=|2x+3|

−x−2−x+3=−2x−3
-2x+1 = -2x-3
1=-3

which is invalid???

RashmiT , you are correct.
My brain clearly was not working well. :dazed :?
Nice catch, +1, thank you, and my apologies.

With two absolute value terms in an equation, you can open mods.

With more than two mods?

If, as here, the answers are before you, use them.

If answers are not before you, use

"Critical Method" see chetan2u, Absolute Modulus, A Better Understanding

and Bunuel , "3-steps approach for complex problems," Absolute Value Modulus, 3-steps approach

And "Graphical Method," chetan2u , Absolute Modulus, A Better Understanding

(You probably know what to do when there are more than two absolute value expressions. I post these links just in case you might need them, but mostly to help people who have not seen the excellent posts to which the links refer.)
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

What is the value of x? |x+2|+|x−3|=|2x+3|   [#permalink] 06 Jan 2018, 13:59
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