tommh wrote:
Bunuel wrote:
What is the value of x?
(1) \(|x+5| = |x+3|\) --> square both sides: \((x+5)^2=(x+3)^2\) --> \(x^2+10 x+25 = x^2+6 x+9\) --> \(4x=-16\) --> \(x=-4\). Sufficient.
(2) \(|x+3| = 1\) --> x + 3 = 1 or x + 3 = -1. Hence, x = -2 or x = -4. Not sufficient.
Answer: A.
Hi Bunuel,
I got the answer A but just by plugging in numbers. I looked at the problem and saw that in order for |x+5| = |x+3| the difference has to be 2. Therefore |-1| = |1|.
|x+5| = 1, x = -4 or -6
|x+3| = 1, x = -4 or -2
We have one answer that fits both, therefore sufficient.
I had the same reasoning as you for statement (2).
Answer. A
Am I correct in my reasoning? I wouldn't have considered squaring both sides as it's not something I've been taught before. Is this just something people know to do?
Hi
tommh,
Quote:
I wouldn't have considered squaring both sides as it's not something I've been taught before. Is this just something people know to do?
Yes, this is a standard method to solve such questions.
You can also solve this question using the modulus/absolute value definition.
Definition: Absolute value of a number is distance from 0.
Example: |x| = 3, we can write it as |x-0| = 3. x: those points whose distance from 0 is 3. So, on number line two points will satisfy the condition => x = -3 or 3
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-3-------------0-------------
3--------------
Example2. |x+3| = 3, we can write it as |x- (-3)| = 3. x: those points whose distance from (-3) is 3 units => x = -6 or 0. Refer: (Example2.jpg)
Now, back to the question.
St.1: |x+5| = |x+3| . This can be written as |x - (-5)| = |x - (-3)|. x is number which is equidistant from (-5) and (-3). => x = -4. No other value will satisfy this condition. Please refer attached diagram (Statement1.jpg) . Hence, sufficient.
St2: |x+3| = 1. |x - (-3)| = 1 => x = -2 or -4. Not sufficient.
Hope it helps.
Thanks.
Attachments
Statement1.jpg [ 102.57 KiB | Viewed 741 times ]
Example2.jpg [ 78.57 KiB | Viewed 740 times ]