For this question I am going to use ~ as the absolute value sign as I cannot type it.
Is ~x~<1?
1. ~x+1~ = 2~x-1~
2. ~x-3~ does not equal 0
Thanks
Is ~x~<1?
1. ~x+1~ = 2~x-1~
2. ~x-3~ does not equal 0
Thanks
Statement 1: This means the distance of x from -1 on the number line is twice the distance of x from 1. Now if you try to draw the scenario on the number line you will see that this is possible in two ways,alex.gellatly wrote:Is |x| < 1?
1. |x + 1| = 2|x - 1|
2. |x - 3| ≠0
- # x lies between -1 and 1.
Hence, |x + 1| = (x + 1) and |x - 1| = -(x - 1) = (1 - x)
Hence, (x + 1) = 2(1 - x) ---> x = 1/3
Or, |x| < 1
# x is greater than 1.
Hence, |x + 1| = (x + 1) and |x - 1| = (x - 1)
Hence, (x + 1) = 2(x - 1) ---> x = 3
Or, |x| > 1
Statement 2: x can be anything except 3.
Not sufficient
1 & 2 Together: x = 1/3 --> |x| < 1
Sufficient
The correct answer is C.
