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# What is the range of the solutions to the equation |2x − 3| = 7?

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Math Expert
Joined: 02 Sep 2009
Posts: 52430
What is the range of the solutions to the equation |2x − 3| = 7?  [#permalink]

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16 Apr 2018, 04:14
00:00

Difficulty:

15% (low)

Question Stats:

67% (00:48) correct 33% (00:52) wrong based on 235 sessions

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What is the range of the solutions to the equation |2x − 3| = 7?

A. 4
B. 5
C. 6
D. 7
E. 8

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Joined: 07 Dec 2017
Posts: 868
Re: What is the range of the solutions to the equation |2x − 3| = 7?  [#permalink]

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16 Apr 2018, 06:37
2
1
Bunuel wrote:
What is the range of the solutions to the equation |2x − 3| = 7?

A. 4
B. 5
C. 6
D. 7
E. 8

We'll simplify the problem stem to understand what we need to do.
This is a Precise approach.

By definition of the absolute value, the expression |2x - 3| = 7 simplifies to 2x - 3 = 7 if 2x - 3 is positive or to 3 - 2x = 7 if 2x - 3 is negative.
In the first case, we can solve for x to get x = 5.
In the second case, solving for x gives -2.
Then our range is 5 - (-2) = 7.

(D) is our answer.
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Joined: 29 Dec 2017
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Location: United States
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Re: What is the range of the solutions to the equation |2x − 3| = 7?  [#permalink]

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16 Apr 2018, 08:50
DavidTutorexamPAL wrote:
Bunuel wrote:
What is the range of the solutions to the equation |2x − 3| = 7?

A. 4
B. 5
C. 6
D. 7
E. 8

We'll simplify the problem stem to understand what we need to do.
This is a Precise approach.

By definition of the absolute value, the expression |2x - 3| = 7 simplifies to 2x - 3 = 7 if 2x - 3 is positive or to 3 - 2x = 7 if 2x - 3 is negative.
In the first case, we can solve for x to get x = 5.
In the second case, solving for x gives -2.
Then our range is 5 - (-2) = 7.

(D) is our answer.

Should we check x as we have to do it in inequalities? Or we have to check when we have more than 1 module? Thanks
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Joined: 07 Dec 2017
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Re: What is the range of the solutions to the equation |2x − 3| = 7?  [#permalink]

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16 Apr 2018, 11:36
Hero8888 wrote:
Should we check x as we have to do it in inequalities? Or we have to check when we have more than 1 module? Thanks

Hi,

Do you mean check the result of x in the original equation?
Yes, if you have the time you can check that x = 5 and x = -2 solve the equation to make sure that you didn't make a calculation mistake.
But you don't have to.... it is partially a question of time and partially that of self-confidence: how sure are you in your result.

Does that answer your question? If not, don't hesitate to ask again.

Best of luck,
David
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Senior Manager
Joined: 29 Dec 2017
Posts: 386
Location: United States
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Re: What is the range of the solutions to the equation |2x − 3| = 7?  [#permalink]

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16 Apr 2018, 13:03
DavidTutorexamPAL wrote:
Hero8888 wrote:
Should we check x as we have to do it in inequalities? Or we have to check when we have more than 1 module? Thanks

Hi,

Do you mean check the result of x in the original equation?
Yes, if you have the time you can check that x = 5 and x = -2 solve the equation to make sure that you didn't make a calculation mistake.
But you don't have to.... it is partially a question of time and partially that of self-confidence: how sure are you in your result.

Does that answer your question? If not, don't hesitate to ask again.

Best of luck,
David

Thank you for the answer. I meant that in inequalities we check x, when we solve module problems. Should we check it in equalities or we don't have constraints?
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Joined: 07 Dec 2017
Posts: 868
Re: What is the range of the solutions to the equation |2x − 3| = 7?  [#permalink]

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16 Apr 2018, 13:24
1
Hero8888 wrote:
DavidTutorexamPAL wrote:
Hero8888 wrote:
Should we check x as we have to do it in inequalities? Or we have to check when we have more than 1 module? Thanks

Hi,

Do you mean check the result of x in the original equation?
Yes, if you have the time you can check that x = 5 and x = -2 solve the equation to make sure that you didn't make a calculation mistake.
But you don't have to.... it is partially a question of time and partially that of self-confidence: how sure are you in your result.

Does that answer your question? If not, don't hesitate to ask again.

Best of luck,
David

Thank you for the answer. I meant that in inequalities we check x, when we solve module problems. Should we check it in equalities or we don't have constraints?

The only constraint in an equality is the 'equal' sign (and anything else that the question tells you like integers/positive/negative etc.)
So if you've found a solution and you're confident there are no calculation mistakes there is no need to check.
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Manager
Joined: 29 Jul 2018
Posts: 107
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Re: What is the range of the solutions to the equation |2x − 3| = 7?  [#permalink]

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28 Aug 2018, 22:16
|2x - 3| = 7
|x - 3/2| = 7/2
origin = 3/2
to find range
add origin and 7/2 = 10/2= 5
and subtract 3/2-7/2 = -4/2 = -2
range = 5 - (-2) = 7
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Posts: 795
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Re: What is the range of the solutions to the equation |2x − 3| = 7?  [#permalink]

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01 Sep 2018, 22:53
Bunuel wrote:
What is the range of the solutions to the equation |2x − 3| = 7?

A. 4
B. 5
C. 6
D. 7
E. 8

|2x − 3| = 7
max => 2x-3=7, x=5
min => 2x-3=-7,x=-2
Range = max - min = 5-(-2) = 7
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Re: What is the range of the solutions to the equation |2x − 3| = 7?  [#permalink]

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02 Sep 2018, 00:04
Bunuel wrote:
What is the range of the solutions to the equation |2x − 3| = 7?

A. 4
B. 5
C. 6
D. 7
E. 8

2x - 3 =7, x = 5
-2x+3 = 7, x = -2

Range = 7
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Re: What is the range of the solutions to the equation |2x − 3| = 7?  [#permalink]

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03 Sep 2018, 18:05
Bunuel wrote:
What is the range of the solutions to the equation |2x − 3| = 7?

A. 4
B. 5
C. 6
D. 7
E. 8

Let’s first solve for when (2x - 3) is positive:

2x - 3 = 7

2x = 10

x = 5

Now let’s solve for when (2x - 3) is negative:

-(2x - 3) = 7

-2x + 3 = 7

-2x = 4

x = -2

Therefore, the range of the solutions is 5 - (-2) = 7.

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Re: What is the range of the solutions to the equation |2x − 3| = 7? &nbs [#permalink] 03 Sep 2018, 18:05
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# What is the range of the solutions to the equation |2x − 3| = 7?

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