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u can do this way. Directly substitute the value of x by trial and error method . Start from 0 and move on. u will get 0,1 and 2 as it asked for positive integers

Re: How many possible integer values are there for x, if I 4x 3 [#permalink]

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19 Oct 2013, 22:28

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What I did here was to separate two scenarios: a. 4x – 3 < 6 and b. 4x – 3 > - 6

I simplified x in both scenarios that I ended up in a range of -2.25 < x < .75 Therefore, my answer is 3 integers (-2, -1, 0)

I would like to know if this method is correct and if I should use such method for problems that involve absolute value and inequality.

You can try algebraically, If x>=0, then you will have the range 0<=x<9/4 If x<0, you get x>3/4 but this solution is not valid so x must vbe x>=0. Hence, you have 3 integer solutions from the above inequality: 0, 1 and 2.

Re: How many possible integer values are there for x if |4x - 3| [#permalink]

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11 Apr 2014, 06:29

My Strategy , X is an integer ( + , - , 0 ) Principles : Integers ,Module and Inequality Plug In Method Start with 0 , 1 , -1 , 2 as values By Plugging in |4x - 3| < 6 Is Yes for 0 , 1, 2 But not with -1 So 3 Values

After seeing Bunnel solution we can use Module Basics with a Range in Number line -6<4x - 3< 6 , -3<4x<9 , \frac {3}{4} <x< \frac{9}{4}, So - 0,75<x< 2.25 So Range from 0 , 1 , 2

If any wrong or any Suggestions in my Strategy pls Correct it
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Re: How many possible integer values are there for x if |4x - 3| [#permalink]

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11 Apr 2014, 11:12

kanusha wrote:

My Strategy , X is an integer ( + , - , 0 ) Principles : Integers ,Module and Inequality Plug In Method Start with 0 , 1 , -1 , 2 as values By Plugging in |4x - 3| < 6 Is Yes for 0 , 1, 2 But not with -1 So 3 Values

After seeing Bunnel solution we can use Module Basics with a Range in Number line -6<4x - 3< 6 , -3<4x<9 , \frac {3}{4} <x< \frac{9}{4}, So - 0,75<x< 2.25 So Range from 0 , 1 , 2

If any wrong or any Suggestions in my Strategy pls Correct it

your strategy is good but suppose if you have lot of integers, how many will you keep plugging?

The second method is better as you quickly know the range and based on conceptual understanding.

given 4x - 3 can take both positive and negative values. It can lie between -6 and 0 or 0 and +6.

Re: How many possible integer values are there for x if |4x - 3| [#permalink]

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27 Apr 2014, 08:58

Bunuel wrote:

How many possible integer values are there for x if |4x - 3| < 6 ?

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

\(|4x - 3| < 6\);

Get rid of the modulus: \(-6<4x-3< 6\);

Add 3 to all three parts: \(-3<4x< 9\);

Divide by 4: \(-\frac{3}{4}<x< \frac{9}{4}\) --> \(-0.75<x< 2.25\).

x can take following integer values: 0, 1, and 2.

Answer: C.

@Bunuel - The question stems talks about how many positive integer values of x. IF we are talking about positive integer then it should be only {1,2} and not {0). Am I missing anything here?

How many possible integer values are there for x if |4x - 3| < 6 ?

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

\(|4x - 3| < 6\);

Get rid of the modulus: \(-6<4x-3< 6\);

Add 3 to all three parts: \(-3<4x< 9\);

Divide by 4: \(-\frac{3}{4}<x< \frac{9}{4}\) --> \(-0.75<x< 2.25\).

x can take following integer values: 0, 1, and 2.

Answer: C.

@Bunuel - The question stems talks about how many positive integer values of x. IF we are talking about positive integer then it should be only {1,2} and not {0). Am I missing anything here?

The question does not specify that the integers must be positive: "how many possible integer values are there for x..."

Re: How many possible integer values are there for x if |4x - 3| [#permalink]

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28 Apr 2014, 05:46

Bunuel wrote:

chanakya84 wrote:

Bunuel wrote:

How many possible integer values are there for x if |4x - 3| < 6 ?

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

\(|4x - 3| < 6\);

Get rid of the modulus: \(-6<4x-3< 6\);

Add 3 to all three parts: \(-3<4x< 9\);

Divide by 4: \(-\frac{3}{4}<x< \frac{9}{4}\) --> \(-0.75<x< 2.25\).

x can take following integer values: 0, 1, and 2.

Answer: C.

@Bunuel - The question stems talks about how many positive integer values of x. IF we are talking about positive integer then it should be only {1,2} and not {0). Am I missing anything here?

The question does not specify that the integers must be positive: "how many possible integer values are there for x..."

Re: How many possible integer values are there for x if |4x - 3| [#permalink]

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03 Nov 2015, 03:30

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