SOLUTION: 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

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.

RELATED QUESTIONS
If 3b + 1 < 10, which of the following CANNOT be the value of x? a) -1 b) 0... (answered by richwmiller)

If 3b + 1 < 10, which of the following CANNOT be the value of x? a) -1 b) 0 c) 1 d) 2 (answered by rfer)

if 3b + 1 < 10 which of the following cannot be the value of b ? (A) -1 (B) 0 (C) 1 (answered by checkley77)

For which of the following values of m will the value of 3m - 1 be greater than 10 ? (answered by london maths tutor)

For which of the following values of k will the value of 3k-1 be greater than 10 ?... (answered by checkley77)

for which of the following values of m will the value of 3m � 1 be greater than 10... (answered by josmiceli)

if x = -1 and k > 0, which of the following has the greatest value ? a 2 kx b... (answered by stanbon)

. For any numbers a and b , a#b= a + b �ab . If a#b = 0, which of the following (answered by Edwin McCravy)

| 2 - x | < 3 , which of the following is a possible value of x ? a 4 b 5 c (answered by alicealc)