If x is an integer and y = –2x – 8, what is the least value of x for

In other words, find the smallest INTEGER value of x such that -2x - 8 < 9
Take: -2x - 8 < 9
Add 8 to both sides to get: -2x < 17
Divide both sides by -2 to get: x > -8.5 [NOTE: since we divided by a NEGATIVE value, we reversed the inequality symbol]
The smallest INTEGER that's greater than -8.5 is -8

Answer:

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Go through the options , here the options are arranged in descending order...

(A) y = –2x – 8

Or, y = 18 - 8

Or, y = 10


(B) y = –2x – 8

Or, y = 16 - 8

Or, y = 8 ( Maximum value < 9 )


(C) y = –2x – 8

Or, y = 14 - 8

Or, y = 6


(D) y = –2x – 8

Or, y = 12 - 8

Or, y = 4


(E) y = –2x – 8

Or, y = 10 - 8

Or, y = 2


Thus, answer will be (B)
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y = -2x-8 < 9
-> 2x+8 > -9
-> 2x > -17
-> x> -8.5
Since x is an integer. x =-8

Bunuel, or GMATPrepNow, or any expert, I have a question about how to think about the end result. I solved as GMATPrepNow did:

-2x - 8 < 9
-2x < 17
x > -17/2, or x > -8.5

I couldn't decide, simply from that result and the number line, whether the integer equaling "least value for x" was -9 or -8.

So I plugged x = -9 into original equation. Incorrect. It yields y = 10, but y cannot be greater than 9. x = -8 yields y = 8, which satisfies y < 9.

I rarely have a hard time knowing whether to "round" up or round down.

Here it seemed tricky because x = -9 and x = -8 both satisfy the condition that x > - 8.5. "[L]east value of x" wasn't self-evident. Worse, -9 is smaller than -8, and we're looking for "least" integer.

I'm frustrated. This issue seems relatively simple. Because answer choice (A) is -9, I suspect that trap tempts others.

GMATPrepNow refers to "the smallest [integer] that's greater than -8.5 . . ." How do we know, intuitively or otherwise, to choose the value for x that's greater than -8.5? I'm missing something really obvious, I think. Sorry. (Then again, "Don't ask, don't know.")
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After you get x > -8.5, think this way. You need the smallest x, which is greater than -8.5. -9 is not greater than -8.5 but -8 is.
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We need to determine the least value of x such that y < 9. Since y = -2x - 8, we have:

-2x - 8 < 9

-2x < 17

x > -17/2

x > -8.5

Since x must be an integer, its least value is when x = -8.

Answer: B
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\(x\) is an integer and

\(y = –2x – 8\)

Since we need to find least value of \(x\) where \(y < 9\)

\(-2x - 8 < 9\)

\(-2x < 17\)

\(-x < 8.5\)

\(x > -8.5\) (Sign Change)

Since, x is an integer and value of \(x > -8.5\) and we have to find the least value of \(x\) the answer will be \(8\)

Hence, Answer is B
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x is an I, can be +ive or -ive

y = -2x-8

A 18 -8 = 10 < 9 No

B 16 - 8 < 9 Yes

C 14 -8 = 6 < 9 Yes

D 12 - 8 = 4 < 9 Yes

E 10 - 8 = 2 < 9 Yes

Least is B
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simply do plug in and check for values
we observe that at B its true
IMO B

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