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25 May 2017, 22:08
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Do we have any other method than taking random values to solve absolute value questions as mentioned below
|2x+3| = |5x+3/2| , Find the possible values of X.
|2x+3| = |5x+3/2| , Find the possible values of X.
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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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25 May 2017, 23:40
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sriamlan
Dear sriamlan ,
Random Values method is a very risky method of solving modulus questions. You never know which scenario you have missed and thus got your question wrong.
Here is a great post written by our Maths expert: https://gmatclub.com/forum/math-absolut ... 86462.html
Please have a look and reach out for more concerns.
P.S: It talks about Zero point method, which is the best method to get 100% right answer.
08 Jun 2017, 13:35
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sriamlan
One option for a question like this, where you have an equation with just an absolute value on one side and just an absolute value on the other side, is to consider the only two possible cases:
- \(2x+3\) has the same sign as \(5x+\frac{3}{2}\), in which case \(2x+3 = 5x+\frac{3}{2}\) (this also applies if both sides equal 0)
- \(2x+3\) has a different sign than \(5x+\frac{3}{2}\), in which case \(2x+3 = -(5x+\frac{3}{2})\)
Now, we just need to solve the equation for each case, and these will be the solutions to the original equation:
- For the first case, the solution is \(x = \frac{1}{2}\)
- For the second case, the solution is \(x = -\frac{9}{14}\)
So, those are the solutions to this equation. Please note that this method does not work if there is anything besides the absolute value on each side of the equation, such as \(|2x+3| = |5x+\frac{3}{2}| +1\)
Please let me know if you have any questions about this!
Cheers,
Jeff
