Hi,
Suppose I have the below inequality
3-2x>-x+4>7.2-2x
Now if I break these 2 inequalities I get x<-1 or x>3.2... Now if I substitue any one value of x say x=3.2 it does not satisfy the above combined inequality..Why? But if I break up the same combined inequality and if it is negative say 3-2x<-x+4<7.2-2x , then each value of x satisfies the combined inequality.. I know that the < gives me a region on a line segment but was just wondering if each positive value of x should satisfy the combined inequality or this is the way it works with positives.. Am I doing it right ?
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- RonPurewal
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when you break up a combined inequality like that, you must take ONLY the solutions that satisfy BOTH of the component inequalities. you CANNOT take the combined set of values that satisfy either one of them; that's just not how the game is played. when you write a combined inequality like that, you're implying that ALL of the components are true.
so your first inequality would require that x < -1 AND x > 3.2, a condition that is of course impossible.
note that it's fairly transparent that your first set of inequalities should be impossible; if you look at the "bread" of the "sandwich" (i.e., the outer 2 parts), you see 3 - 2x > 7.2 - 2x. that's impossible (the right-hand side is always 4.2 more than the left-hand side), so the whole thing is impossible.
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in your second version (with the signs reversed), you get x > -1 AND x < 3.2. these are perfectly consistent; the solution consists of all those x such that both statements are true, or -1 < x < 3.2.
try any value in that range; it will work.
finally, don't forget that these are INEQUALITIES. they are not equations. therefore, do NOT fixate on values such as x = 3.2, which are not solutions to anything (because "<" and ">" mean strictly less / greater than).
so your first inequality would require that x < -1 AND x > 3.2, a condition that is of course impossible.
note that it's fairly transparent that your first set of inequalities should be impossible; if you look at the "bread" of the "sandwich" (i.e., the outer 2 parts), you see 3 - 2x > 7.2 - 2x. that's impossible (the right-hand side is always 4.2 more than the left-hand side), so the whole thing is impossible.
--
in your second version (with the signs reversed), you get x > -1 AND x < 3.2. these are perfectly consistent; the solution consists of all those x such that both statements are true, or -1 < x < 3.2.
try any value in that range; it will work.
finally, don't forget that these are INEQUALITIES. they are not equations. therefore, do NOT fixate on values such as x = 3.2, which are not solutions to anything (because "<" and ">" mean strictly less / greater than).
3 posts Page 1 of 1