Possible example:
2|x| = x2 - 8
For x>=0,
x2 - 2x - 8 = 0
(x-4)(x+2)=0
so x=4 (can't be -2 since x>=0)
For x<0,
x2 + 2x - 8 = 0
(x-2)(x+4)=0
so x=-4 (can't be 2 since x<0)
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An absolute value may not need a number line to solve. Absolute value means the distance form zero regardless of the sign.
The basic idea here is to look at both equations and solve for either x or y in one of the equations. Then plug the known value into the second equation and solve for the other variable.
An equation with absolute values instead of simple variables has twice as many solutions as an otherwise identical equation with simple variables, because every absolute value has both a negative and a positive counterpart.
The absolute value of a number can be considered as the distance between 0 and that number on the real number line. example. or l2+6l=8 the point is to solve in between the absolute value lines
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