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Re: If x is an integer and |2x+3|12 [#permalink]
Carcass

Upon calculation, x ≤ 4.5

Could you please explain why cant the ans be (D) x< 4 ??
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Re: If x is an integer and |2x+3|12 [#permalink]
Expert Reply
\(2x+3 \leq 12\)

\(2x \leq 9\)

\(x \leq 4.5\)

\(-2x-3 \leq 12\)

\(-2x \leq 15\)

\(x \geq -7.5\)



--------------------- -7.5 -------------------------------------- 4.5 -------------------------

Our range is the blue one.

x< -9

Out of range

x< -8

Out of range

x> -8

goes up from -8 and pass through our range completely. covering all the values

x< 4

goes down but DO NOT cover all the range because we are off the points between 4.5 and 4 downward

x> 4

cover the points above 4 to 4.5 and then goes out of our range but does not cover all the points <4 downward to -7.5

I hope this helps
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Re: If x is an integer and |2x+3|12 [#permalink]
Carcass wrote:
\(2x+3 \leq 12\)

\(2x \leq 9\)

\(x \leq 4.5\)

\(-2x-3 \leq 12\)

\(-2x \leq 15\)

\(x \geq -7.5\)



--------------------- -7.5 -------------------------------------- 4.5 -------------------------

Our range is the blue one.

x< -9

Out of range

x< -8

Out of range

x> -8

goes up from -8 and pass through our range completely. covering all the values

x< 4

goes down but DO NOT cover all the range because we are off the points between 4.5 and 4 downward

x> 4

cover the points above 4 to 4.5 and then goes out of our range but does not cover all the points <4 downward to -7.5

I hope this helps



I'm sorry I still didnt understand: how can going up from -8 cover all the values & going down 4 is not sufficient?
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If x is an integer and |2x+3|12 [#permalink]
Expert Reply
x>-8 means from minus 8 up to the infinity on the number line

x < 4 down to the infinity on the number line


--------------------- -7.5 -------------------------------------- 4.5 -------------------------

-8 --- - 7.5 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ >>>

<<<< ------------------------------------------------------------------------------------------------- 4 ----- -4.5

We have the gap between 4.5 and 4. Starting from four we do not have the points between 4 and 4.5
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Re: If x is an integer and |2x+3|12 [#permalink]
1
Carcass wrote:
x>-8 means from minus 8 up to the infinity on the number line

x < 4 down to the infinity on the number line


--------------------- -7.5 -------------------------------------- 4.5 -------------------------

-8 --- - 7.5 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ >>>

------------------------------------------------------------------------------------------------- 4 ----- -4.5

We have the gap between 4.5 and 4. Starting from four we do not have the points between 4 and 4.5


Ohhh. I now understood the logic!
Thanks man :)
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Re: If x is an integer and |2x+3|12 [#permalink]
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