Answers:
x = 48x=48 and x = -12x=−12
Solution:
|2/3x - 1/4x| = |1/4x + 8|∣∣∣23x−14x∣∣∣=∣∣∣14x+8∣∣∣
=> |(8 - 3)/12x| = |1/4x + 8|⇒∣∣∣8−312x∣∣∣=∣∣∣14x+8∣∣∣
=> |5/12x| = |1/4x + 8|⇒∣∣∣512x∣∣∣=∣∣∣14x+8∣∣∣
Square both sides, you get
(5/12x)^2 = (1/4x + 8)^2(512x)2=(14x+8)2
=> (5/12x)^2 - (1/4x + 8)^2 = 0⇒(512x)2−(14x+8)2=0
This is a difference of two squares, as a^2 - b^2 = (a - b)(a + b)a2−b2=(a−b)(a+b)
=> (5/12x - (1/4x + 8))*(5/12x + (1/4x + 8)) = 0⇒(512x−(14x+8))⋅(512x+(14x+8))=0
=> ( 2/12x - 8)(8/12x + 8) = 0⇒(212x−8)(812x+8)=0
=> 2/12x - 8 = 0 => 1/6x = 8 => x = 48⇒212x−8=0⇒16x=8⇒x=48
Also,
8/12x + 8 = 0 => 2/3x = -8 => x = -12812x+8=0⇒23x=−8⇒x=−12
