Question 552653: 4x < 4... I say x=1, my son says it is -1
Who is right?!
Thanks
Found 2 solutions by AnlytcPhil, Edwin McCravy:
Answer by AnlytcPhil(1807)   (Show Source):
You can put this solution on YOUR website! There previously was an error in the solution, which has now been corrected.
You are thinking about equations, not inequalities. If 4x is less than 4,
which is what 4x < 4 means, then x is less than 1. It cannot be equal to 1.
In fact x is a variable, and it is not necessarily equal to any one number.
x could be any number less than 1. It could be  , or 0 or 0.7, or -1,
or -46, or -10000000 or -9 or .... Yes it could be -1, but certainly not
necessarily.
There is no one number that x can only be, because x is a variable, and can
vary its value to any number less than 1.
We make a number line, and shade the part x can be. It cannot be 1,
so we put an open circle there
<==================o------------------
-5 -4 -3 -2 -1 0 1 2 3 4 5
That is the graph of the solution set of the inequality 4x < 4 or x < 1
Edwin
Answer by Edwin McCravy(20062)  (Show Source):
You can put this solution on YOUR website! There previously was an error in this solution, which has now been corrected.
You are thinking about equations, not inequalities. If 4x is less than 4,
which is what 4x < 4 means, then x is less than 1. It cannot be equal to 1.
In fact x is a variable, and it is not necessarily equal to any one number.
x could be any number less than 1. It could be , or 0 or 0.7, or -1,
or -46, or -10000000 or -9 or .... Yes it could be -1, but certainly not
necessarily.
There is no one number that x can only be, because x is a variable, and can
vary its value to any number less than 1.
We make a number line, and shade the part x can be. It cannot be 1,
so we put an open circle there
<==================o------------------
-5 -4 -3 -2 -1 0 1 2 3 4 5
That is the graph of the solution set of the inequality 4x < 4 or x < 1
Edwin
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