Given that |x - 2| = |x + 3| and we need to find the value of xLet's solve this using three methods
Method 1: SubstitutionLet's take values in each answer choice and substitutive in the equation and check which one satisfies the equation
A. -5 Put x = -5 in |x - 2| = |x + 3| and check if it satisfies the equation
=> |-5 - 2| = |-5 + 3| => |-8| = |-2|
=> 8 = 2 => FALSE
B. -1/2 Put x = -1/2 in |x - 2| = |x + 3| and check if it satisfies the equation
=> |-1/2 - 2| = |-1/2 + 3| => |-5/2| = |5/2|
=> 5/2 = 5/2 => TRUE
We don't need to check further as the question has asked for only one value
Method 2: Algebra|x - 2| = |x + 3|
Square both the sides we get
\((|x-2|)^2 = (|x+3|)^2\)
=> \((x-2)^2 = (x+3)^2\)
=> \(x^2 -2*x*2 + 2^2 = x^2 + 2*x*3 + 3^2\)
=> \(x^2 -2*x*2 + 2^2 - x^2 - 2*x*3 - 3^2\) = 0
=> -4x + 4 - 6x - 9 = 0
=> -10x = 5
=> x = \(\frac{-5}{10}\) = \(\frac{-1}{2}\)
Method 3: Graphical Method|x - 2| = Distance between x and 2
|x + 3| = | x - (-3)| = Distance between x and -3
Attachment:
-3 to 2.JPG [ 16.47 KiB | Viewed 3701 times ]
So, for Distance between x and 2 = Distance between x and -3
x has to be at the mid-point of -3 and 2
=> x = \(\frac{-3+2}{2}\) = \(\frac{-1}{2}\)
So,
Answer will be BHope it helps!
Watch the following video to learn How to Solve Absolute Value Problems