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

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Math Expert
Joined: 02 Sep 2009
Posts: 59721
How many values of x are there such that x is an integer and |3x - 2|  [#permalink]

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22 Nov 2019, 03:26
00:00

Difficulty:

35% (medium)

Question Stats:

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

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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

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Joined: 12 Sep 2015
Posts: 4151
Re: How many values of x are there such that x is an integer and |3x - 2|  [#permalink]

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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.

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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