Maybe you should plot a graph
Which one of the following is not a solution to the equation above?
A) -2.4
B) 4
C)0.8
D) 1.2
E)-1.33333.......
This is a problem from the 2015 mathematics challenge held by Lincoln University.
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1 solution
The equation can be split into 4 equations, each of which has a distinct solution: EQUATIONS: 0 . 2 5 ( x + 4 ) = ( x − 2 ) , 0 . 2 5 ( x + 4 ) = ( − x + 2 ) , 0 . 2 5 ( x + 4 ) = ( x + 2 ) , 0 . 2 5 ( x + 4 ) = ( − x − 2 )
The left sides of all the equations are derived by dividing both sides by 4 . The right sides of both equations are derived from visualizing how the function ∣ ∣ x ∣ − 2 ∣ behaves. ∣ x ∣ − 2 means translating the function ∣ x ∣ down 2 units, and taking the absolute value of that means that all values of y where − 2 < x < 2 are reflected over the x axis. Thus, 4 equations are formed, which are split into the right sides of all the equations. By solving each of them, x = 1 . 2 is not a value of any of the equations.