Question 1050825: The solution set of the equation |2x|=|10x| is given by:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i believe that the only solution to this equation is when x = 0.
the basic definition of absolute value is:
|a| is equal to a when a is positive and is equal to -a when a is negative.
the absolute value of an expression will always be positive.
if the expression is positive, the absolute value of the expression is equal to the expression.
if the expression is negative, the absolute value of the expression is equal to -1 * the expression.
we start with |2x| = |10x|
by definition |10x| = 10x if x is positive and is equal to -10x if x is negative.
by definition |2x| = 2x if x is positive and is equal to -2x if x is negative.
you have 4 possibilities.
2x = 10x
2x = -10x
-2x = 10x
-2x = -10x
you can reduce this to 2 possibilities, because 2 of the equations are equivalent to the other 2.
2x = -10x is equivalent to -2x = 10x because, if you multiply both sides of -2x = 10x by -1, you get 2x = -10x.
likewise, 2x = 10x is equivalent to -2x = -10x because, if you multiply both sides of -2x = -10x by -1, you get 2x = 10x.
you therefore have 2 possibilities.
they are:
2x = 10x
2x = -10x
if you solve for x in both equations, you will find that x = 0 is the only solution applicable to each of those equations.
therefore, the only solution set possible for |2x| = |10x| is x = 0.
if you graph y = |2x| and y = |10x|, you will see that the only intersection of the lines created by those 2 equations is when x = 0.
here's the graph.
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