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How many values of x are there such that x is an integer and |3x - 2|

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How many values of x are there such that x is an integer and |3x - 2|  [#permalink]

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New post 22 Nov 2019, 03:26
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

63% (01:20) correct 37% (01:18) wrong based on 60 sessions

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Re: How many values of x are there such that x is an integer and |3x - 2|  [#permalink]

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New post 22 Nov 2019, 07:48
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Top Contributor
1
Bunuel wrote:
How many values of x are there such that x is an integer and \(|3x — 2| < 8\)?

A. One
B. Two
C. Three
D. Four
E. Five


---------ASIDE---------------------
When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:
Rule #1: If |something| < k, then –k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k

Note: these rules assume that k is positive
------------------------------------

Take: \(|3x — 2| < 8\)
Applying Rule #1, we can write: \(-8 < 3x — 2 < 8\)

Add 2 to all sides to get: \(-6 < 3x < 10\)

Divide all sides by 3 to get: \(-2 < x < \frac{10}{3}\)

In other words: \(-2 < x < 3 \frac{1}{3}\)

So, the INTEGER values of \(x\) that satisfy the above inequality are: \(x = -1, 0, 1, 2\) and \(3\)

There are FIVE such values.

Answer: E

Cheers,
Brent
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Re: How many values of x are there such that x is an integer and |3x - 2|   [#permalink] 22 Nov 2019, 07:48
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