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If |4x−4|=|2x+30|, which of the following could be a value of x?

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Bunuel
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If |4x−4|=|2x+30|, which of the following could be a value of x? [#permalink] New post   04 May 2016, 01:46
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If |4x−4|=|2x+30|, which of the following could be a value of x?

A. –17
B. −21/2
C. −13/3
D. 2
E. 15
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C
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KarishmaB
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Re: If |4x−4|=|2x+30|, which of the following could be a value of x? [#permalink] New post   04 May 2016, 21:01
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Bunuel wrote:
If |4x−4|=|2x+30|, which of the following could be a value of x?

A. –17
B. −21/2
C. −13/3
D. 2
E. 15


Just plug in the options.
Options (A), (D) and (E) are quite easy to see. They don't give equal values on LHS and RHS.

With (B), (C), plug in values close to these instead of these fractions.

(B) -21/2
Try x = -10.
You get 50 = 10
The difference between LHS and RHS is quite large so x will not be -21/2. As we go toward the point where LHS = RHS, the difference between them will keep decreasing. Hence a point very close to the actual value of x will have little difference between LHS and RHS.

(C) -13/3
Try x = -4
You get 20 = 22
These are quite close so this will be the answer. You can plug it in to confirm.

Answer (C)
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Re: If |4x−4|=|2x+30|, which of the following could be a value of x? [#permalink] New post   04 May 2016, 20:31
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4x - 4 = 2x + 30 or 4x - 4 = -2x - 30
2x = 34 or 6x = -26
x = 17 or x = -13/3

Answer: C
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Mamyan94
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If |4x−4|=|2x+30|, which of the following could be a value of x? [#permalink] New post   23 Sep 2016, 12:22
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|4x−4|=|2x+30|; 2*|2x-2|=2*|x+15|; |2x-2|=|x+15|

For me the fastest way is to just open the brackets; we have 2 ways to do it

1) 2x-2=x+15 => x=17 => NO
2) 2-2x=x+15=> x=-13/3 => Answer C

for me opening brackets 2 times and solving for such easy numbers is faster than plugging in any of given answers

Hope this helps
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Re: If |4x−4|=|2x+30|, which of the following could be a value of x? [#permalink] New post   16 Apr 2019, 16:04
Are there four different solutions to this?

a = b
-a = b
a = -b
-a = -b
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If |4x−4|=|2x+30|, which of the following could be a value of x? [#permalink] New post   17 Apr 2019, 19:03
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edlc313 wrote:
Are there four different solutions to this?

a = b
-a = b
a = -b
-a = -b


Yes and no. Theoretically that is right, but if you look closely there are actually 2 pairs of solutions each one with 2 expressions that are equivalent:

\(a = b\) is equivalent to \(-a = -b\); and
\(-a = b\) is equivalent to \(a = -b\)
(think that if you multiply one by -1 you get the other)

Hence, there is no need to evaluate four different solutions! All you need to do is to find 2 of them!

\(|4x−4|=|2x+30|\)

(1) a=b

\((4x−4)=(2x+30)\)
\(2x = 34\)
\(x = 17\)

or (2) -a=b

\(-(4x−4)=(2x+30)\)
\(-6x = 26\)
\(x = -13/3\)

Answer: C
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If |4x−4|=|2x+30|, which of the following could be a value of x? [#permalink] New post   07 May 2019, 08:04
VeritasKarishma wrote:
Bunuel wrote:
If |4x−4|=|2x+30|, which of the following could be a value of x?

A. –17
B. −21/2
C. −13/3
D. 2
E. 15


Just plug in the options.
Options (A), (D) and (E) are quite easy to see. They don't give equal values on LHS and RHS.

With (B), (C), plug in values close to these instead of these fractions.

(B) -21/2
Try x = -10.
You get 50 = 10
The difference between LHS and RHS is quite large so x will not be -21/2. As we go toward the point where LHS = RHS, the difference between them will keep decreasing. Hence a point very close to the actual value of x will have little difference between LHS and RHS.

(C) -13/3
Try x = -4
You get 20 = 22
These are quite close so this will be the answer. You can plug it in to confirm.

Answer (C)


Hello Ma'am,

Can you explain how to represent these sort of numericals graphically on the number line?

Posted from my mobile device
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Re: If |4x−4|=|2x+30|, which of the following could be a value of x? [#permalink] New post   08 May 2019, 02:41
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AMP2021 wrote:
VeritasKarishma wrote:
Bunuel wrote:
If |4x−4|=|2x+30|, which of the following could be a value of x?

A. –17
B. −21/2
C. −13/3
D. 2
E. 15


Just plug in the options.
Options (A), (D) and (E) are quite easy to see. They don't give equal values on LHS and RHS.

With (B), (C), plug in values close to these instead of these fractions.

(B) -21/2
Try x = -10.
You get 50 = 10
The difference between LHS and RHS is quite large so x will not be -21/2. As we go toward the point where LHS = RHS, the difference between them will keep decreasing. Hence a point very close to the actual value of x will have little difference between LHS and RHS.

(C) -13/3
Try x = -4
You get 20 = 22
These are quite close so this will be the answer. You can plug it in to confirm.

Answer (C)


Hello Ma'am,

Can you explain how to represent these sort of numericals graphically on the number line?

Posted from my mobile device


If you mean how to solve this using the number line concept,

|4x−4|=|2x+30|
4*|x−1|=2|x+15|
2*|x - 1| = |x + 15|

Twice the distance from 1 is equal to distance from -15. So the distance of 16 is divided into 3 equal parts such that x is 1 part away from 1.

x = 1 - 16/3 = -13/3

If you understand above, the solution will take just a few seconds else it might be easier to plug in values here or square both sides.
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Re: If |4x−4|=|2x+30|, which of the following could be a value of x? [#permalink] New post   01 Mar 2022, 04:08
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KarishmaB

can you explain how you got to 1-16/3?

Why is it not 16/3?

Thanks a lot!
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Re: If |4x−4|=|2x+30|, which of the following could be a value of x? [#permalink] New post   01 Mar 2022, 05:01
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Hunter2021 wrote:
KarishmaB

can you explain how you got to 1-16/3?

Why is it not 16/3?

Thanks a lot!



2*|x - 1| = |x + 15|

means

x is a point such that twice its distance from 1 is equal to its distance from -15

Attachment:
Screenshot 2022-03-01 at 17.24.34.png
Screenshot 2022-03-01 at 17.24.34.png [ 17.84 KiB | Viewed 3304 times ]


Distance from 1 is the red line. Twice of that should be equal to the blue line (distance from - 15).

How will you find what x is? We divide 16 into 3 equal parts. The red line is 1 part and the blue line is 2 parts. So x is 1 part behind 1 on the number line.
So x is 1 - 16/3

I have discussed this in detail in my inequalities and absolute values module. You can check out the preview here:
https://anglesandarguments.com/study-module
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Re: If |4x−4|=|2x+30|, which of the following could be a value of x? [#permalink] New post   01 Mar 2022, 13:16
Whenever \(|a|=|b|\) either \(a=b\) or \(a=-b\)

Since we've been given that \(|4x-4|=|2x+30|\) therefore

Case 1: \(4x-4=2x+30\) which means \(2x=34\) or \(x=17\)

Case 2: \(4x-4=-2x-30\) which means \(6x=-26\) or \(x=-13/3\)

Out of these two only \(-13/3\) is present in the options and hence is our answer.

Hence, C.

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Re: If |4x−4|=|2x+30|, which of the following could be a value of x? [#permalink]
01 Mar 2022, 13:16
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