Carcass wrote:
\(|x-2| > 3\)
Quantity A |
Quantity B |
The minimum possible value of |x - 3.5| |
The minimum possible value of | x - 1.5 | |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
\(|x-2| > 3\)
we can find the values of x in three ways...
(I) Since both sides are positive, square both sides\(|x-2|^2 > 3^2.......x^2-4x+4>9.........x^2-4x-5>0.....x^2-5x+x-5>0........(x+1)(x-5)>0\)
a) either both are positive.. x+1>0 and x-5>0, so x>-1 and x>5...x>5
b) or both are negative .. x+1<0 and x-5<0, so x<-1 and x<5 ... so x<-1
x<-1 and x>5
(II) critical point..x<=2..... -(x-2)>3.......x-2<-3....x<-1
x>2...... (x-2)>3......x>5
(III) logical approach via number line..\(|x-2| > 3\) means the distance of x from 2 is greater than 3 units..
so if x is on the left side of 2, it will be < (2-3) or <-1
if x is on the right side of 2, it will be > (2+30 or >5
you can learn more of this from
https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.htmlso we have range of x as x<-1 and x>5
The minimum possible value of |x - 3.5| ... again which value in range is closer to 3.5, it is 5, so value is just > |5-3.5| or just > 1.5
The minimum possible value of | x - 1.5 |... again which value in range is closer to 1.5, it is -1, so value is just > |-1-1.5| or just > 2.5
so B>A
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html