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Question 259691: If -6 < 2 - 3x < 10 , which of the following can not be a possible value of x?
(A) -3 (B) -2 (C) -1 (D) 0 (E) 2
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! -6 < 2-3x < 10 is your equation:
subtract 2 from all sides of the equation to get:
-8 < -3x < 8
multiply all sides of the equation by -1 to get:
8 > 3x > -8
divide all sides of the equation by 3 to get:
8/3 > x > -8/3
you have:
x > -8/3 and x < 8/3
this translates to:
x > -2.66666666... and x < 2.66666666...
unless it gets real close, I'll use x > -2.6 and x < 2.6 as the limits test.
when x = -3, x is smaller than -2.6 so x = -3 is NOT valid.
when x = -2, x > -2.6 and x < 2.6 so this is good.
when x = -1, x > -2.6 and x < 2.6 so this is good.
when x = 0, x > -2.6 and x < 2.6 so this is good.
when x = 2, x > -2.6 and x < 2.6 so this is good.
looks like selection A is the invalid one.
to confirm, plug that value of x into your original equation.
original equation is:
-6 < 2-3x < 10
substitute (-3) for x into that equation to get:
-6 < 2 - (3*(-3)) < 10 which becomes:
-6 < 2 - (-9) < 10 which becomes:
-6 < 2 + 9 < 10 which becomes:
-6 < 11 < 10.
-6 is smaller than 11 so that part is good.
11 is NOT smaller than 10 so that part is NOT good.
This confirms that selection A cannot be a possible value of x.
If you plug all the other possible values of x into the original equation, you will see that they can be possible values of x.
your answer is selection A.
you showed selection E as 2 A.
I assumed this was a typographical error so I took out the A and left the 2 to make selection E = 2.
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