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Bunuel
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What is the range of the solutions to the equation |2x − 3| = 7? 16 Apr 2018, 05:14
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D
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74% (00:51) correct 26% (00:56) wrong based on 782 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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D
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What is the range of the solutions to the equation |2x − 3| = 7? 16 Apr 2018, 07:37
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Bunuel
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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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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What is the range of the solutions to the equation |2x − 3| = 7? 16 Apr 2018, 09:50
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Bunuel
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.
Show more

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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What is the range of the solutions to the equation |2x − 3| = 7? 16 Apr 2018, 12:36
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Hero8888

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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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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What is the range of the solutions to the equation |2x − 3| = 7? 16 Apr 2018, 14:03
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DavidTutorexamPAL
Hero8888

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
Show more

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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What is the range of the solutions to the equation |2x − 3| = 7? 16 Apr 2018, 14:24
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Hero8888
DavidTutorexamPAL
Hero8888

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?
Show more

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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What is the range of the solutions to the equation |2x − 3| = 7? 28 Aug 2018, 23:16
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|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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What is the range of the solutions to the equation |2x − 3| = 7? 01 Sep 2018, 23:53
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Bunuel
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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|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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What is the range of the solutions to the equation |2x − 3| = 7? 02 Sep 2018, 01:04
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Bunuel
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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2x - 3 =7, x = 5
-2x+3 = 7, x = -2

Range = 7
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What is the range of the solutions to the equation |2x − 3| = 7? 03 Sep 2018, 19:05
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Bunuel
What is the range of the solutions to the equation |2x − 3| = 7?

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

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.

Answer: D
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What is the range of the solutions to the equation |2x − 3| = 7? 16 May 2021, 01:56
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Thanks for the explanation.
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What is the range of the solutions to the equation |2x − 3| = 7? 11 Apr 2024, 02:22
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