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If |3x - 1| = x + 5. Find the value(s) of x ? A. 3 B. 1 C.

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If |3x - 1| = x + 5. Find the value(s) of x ? A. 3 B. 1 C. [#permalink] New post   26 Jun 2019, 05:17
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If |3x - 1| = x + 5. Find the value(s) of x ?

A. 3
B. 1
C. 3, 1
D. 3, -1
E. -1

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D
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Re: If |3x - 1| = x + 5. Find the value(s) of x ? A. 3 B. 1 C. [#permalink] New post   26 Jun 2019, 07:02
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| 3x-1 | = (3x-1) or -3x+1
So 3x-1 = x+5 , x=3
Again -3x+1 = x+5, x= -1
X is 3,-1
Answer D

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If |3x - 1| = x + 5. Find the value(s) of x ? A. 3 B. 1 C. [#permalink] New post   26 Jun 2019, 08:09
Dillesh4096 wrote:
If |3x - 1| = x + 5. Find the value(s) of x ?

A. 3
B. 1
C. 3, 1
D. 3, -1
E. -1

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Two cases-

3x-1= x+5
1-3x= X+5

Just put the values and check in the original equation.



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Re: If |3x - 1| = x + 5. Find the value(s) of x ? A. 3 B. 1 C. [#permalink] New post   28 Jun 2019, 00:24
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Solution



Given:
    • |3x - 1| = x + 5

To find:
    • Value(s) of x.

Approach and Working:
    • For 3x-1 >= 0 or x >\(\frac{1}{3}\), 3x-1= x+ 5
      o 2x =6, x =3
    • For 3x -1< 0, or x < \(\frac{1}{3}\), 3x-1 = -(x+5)
      o 4x =-4, x =-1

Thus, x = -1, 3

Hence, the correct answer is option D.

Answer: D
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Re: If |3x - 1| = x + 5. Find the value(s) of x ? A. 3 B. 1 C. [#permalink] New post   28 Jun 2019, 00:28
Expert Reply
We have also posted an article to show the various approach to solve an absolute value equation.

To read the article: Different methods to solve absolute value equations and inequalities
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Re: If |3x - 1| = x + 5. Find the value(s) of x ? A. 3 B. 1 C. [#permalink] New post   28 Jun 2019, 00:47
Dillesh4096 wrote:
If |3x - 1| = x + 5. Find the value(s) of x ?

A. 3
B. 1
C. 3, 1
D. 3, -1
E. -1

Posted from my mobile device


|3x - 1| = 3x-1 or |3x - 1| = -3x+1 and therefore 2 values of x with both 3 and-1
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Re: If |3x - 1| = x + 5. Find the value(s) of x ? A. 3 B. 1 C. [#permalink] New post   06 Jan 2022, 05:57
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Re: If |3x - 1| = x + 5. Find the value(s) of x ? A. 3 B. 1 C. [#permalink]
06 Jan 2022, 05:57
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