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If x is an integer, what is the value of x such that |-5x + 7| is mini

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If x is an integer, what is the value of x such that |-5x + 7| is mini  [#permalink]

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New post 10 Aug 2018, 02:32
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If x is an integer, what is the value of x such that |-5x + 7| is mini  [#permalink]

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New post 10 Aug 2018, 02:36
Bunuel wrote:
If x is an integer, what is the value of x such that |-5x + 7| is minimized?

A. 0
B. 1
C. 2
D. 3
E. 4



Back solve the question. Scan each answer choice. Only option B works here.
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Re: If x is an integer, what is the value of x such that |-5x + 7| is mini  [#permalink]

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New post 10 Aug 2018, 02:46
1
Bunuel wrote:
If x is an integer, what is the value of x such that |-5x + 7| is minimized?

A. 0
B. 1
C. 2
D. 3
E. 4


Minimum value of |-5x + 7| is zero
Or, |-5x + 7|=0
Or, -5x+7=0
Or, -5x=-7
Or, x=7/5=1.4

So, integer value less than 1.4 is 1.
So, when x=1, |-5x + 7|=|-5+7|=2

Ans. (B)
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If x is an integer, what is the value of x such that |-5x + 7| is mini  [#permalink]

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New post 13 Aug 2018, 06:53

Solution


Given:
    • We are given an expression, |-5x + 7|
    • x is an integer

To find:
    • Value of x, such that |-5x + 7| is minimum

Approach and Working:
    • The minimum value of a modulus function is 0.
    • So, |-5x + 7| will be equal to 0, when x = 7/5 = 1.4
    • But, we need to find an integer value of x, for which |-5x + 7| is minimum
    • Since, the value of |-5x + 7|increases for both x > 1.4 and x < 1.4, so we need to check its value for the integers close to 1.4, which are 1 and 2.
      o For x = 1, the value of |-5x + 7| is 2
      o For x = 2, the value of |-5x + 7| is 3

Therefore, the value of |-5x + 7| is minimum when x = 1

Hence, the correct answer is option B

Answer: B

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If x is an integer, what is the value of x such that |-5x + 7| is mini  [#permalink]

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New post 18 Aug 2018, 18:29
Bunuel wrote:
If x is an integer, what is the value of x such that |-5x + 7| is minimized?

A. 0
B. 1
C. 2
D. 3
E. 4


Recall that the smallest possible value of an absolute value expression is zero. Thus, to minimize |-5x + 7|, we need to get |-5x + 7| as close to zero as possible.

When x is 1, we have:

|-5(1) + 7| = |2| = 2, which is the smallest we can make the given expression when x is an integer.

Answer: B
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Re: If x is an integer, what is the value of x such that |-5x + 7| is mini  [#permalink]

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New post 18 Aug 2018, 18:42
We can substitute for x and check. When x= 0 ,we get 7,
When x=1,we get 2
When x=2,we get 3
We can stop here and conclude that B is the correct choice.

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Re: If x is an integer, what is the value of x such that |-5x + 7| is mini  [#permalink]

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New post 18 Aug 2018, 19:15
Bunuel wrote:
If x is an integer, what is the value of x such that |-5x + 7| is minimized?

A. 0
B. 1
C. 2
D. 3
E. 4


What is the minimum value of any absolute value? 0.
|-5x + 7| = 0
x = 7/5
But we need x to be an integer. 7/5 lies between 1 and 2, closer to 1. So when x = 1, |-5x + 7| will take the minimum value.

If you are not sure why, think of what the graph of y = |-5x + 7| would look like. It will be a symmetrical V resting on x = 7/5. The value of y will continuously increase on both sides of x = 7/5. When you move to the left on the x axis, at x = 1, y will be 2. When you move to the right on the x axis, at x = 2, y will be 3.
The minimum value for an integer value of x will be y = 2 for x = 1.
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Re: If x is an integer, what is the value of x such that |-5x + 7| is mini  [#permalink]

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New post 18 Aug 2018, 19:24
Bunuel wrote:
If x is an integer, what is the value of x such that |-5x + 7| is minimized?

A. 0
B. 1
C. 2
D. 3
E. 4


Responding to a pm:

Quote:
I am stuck b/w A and B. If they are looking for minimum value when you plug in A you get + / - 7 and with B you get +-2. So shouldn't the answer be A given that -7 is less than -2. (or minimum value.)??


We are looking for the minimum value of |-5x + 7|.
If we put x = 0, |-5x + 7| = |-5*0 + 7| = 7
Note that |7| is NOT 7 or -7.
|7| and |-7| both are equal to 7 ONLY

If we put x = 1, |-5x + 7| = |-5*1 + 7| = 2 ONLY

You are getting confused with the definition of absolute values:

|x| = x if x >= 0
|x| = -x if x < 0

So if x = 5, |x| = x = 5 (because x > 0)
If x = -5, |x| = -x = - (-5) = 5 (because x < 0)

That is the whole point of absolute value: It is never negative. It is the distance in physical terms so it cannot be negative.
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Re: If x is an integer, what is the value of x such that |-5x + 7| is mini  [#permalink]

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New post 17 Nov 2018, 01:50
VeritasKarishma wrote:
Bunuel wrote:
If x is an integer, what is the value of x such that |-5x + 7| is minimized?

A. 0
B. 1
C. 2
D. 3
E. 4


What is the minimum value of any absolute value? 0.
|-5x + 7| = 0
x = 7/5
But we need x to be an integer. 7/5 lies between 1 and 2, closer to 1. So when x = 1, |-5x + 7| will take the minimum value.

If you are not sure why, think of what the graph of y = |-5x + 7| would look like. It will be a symmetrical V resting on x = 7/5. The value of y will continuously increase on both sides of x = 7/5. When you move to the left on the x axis, at x = 1, y will be 2. When you move to the right on the x axis, at x = 2, y will be 3.
The minimum value for an integer value of x will be y = 2 for x = 1.


math to english:

|x - 5| = 10 means "the distance of x is 10 centered around 5"

what does |-5x + 7| mean?
is this correct: distance of -5x centered around 7

regards
GMAT Club Bot
Re: If x is an integer, what is the value of x such that |-5x + 7| is mini &nbs [#permalink] 17 Nov 2018, 01:50
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