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

Question

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

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

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.

Bunuel · Accepted Answer

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.

rakesh1239 · Answer

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

lovely_baby · Answer

Cpcalanoc you choose the right way BUT from 4x-3<6 => 4x<9 =>
x<2.25
the same mistake in the other

So -0.75 < x < 2.25
then the answer (0, 1, 2)

to Rakesh1239 your answer is right but where you see the word positive?

jlgdr · Answer

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. Hope this helps Cheers J

email2vm · Answer

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.

kanusha · Answer

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}

ind23 · Answer

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.

chanakya84 · Answer

@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?

Bunuel · Answer

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

Hope it's clear.

chanakya84 · Answer

Ahh..my mistake....
Read the question wrong.

law258 · Answer

You can figure this out by taking the equation and solving:

SCENARIO 1:
(4x - 3) < 6
4x<9
x<(9/4)

SCENARIO 2:
(4x - 3) > -6
4x>-3
x>(-3/4)

So (-0.75)<x<2.25 --> The only integers within this range are 0,1,2 --> Hence, 3 is the correct answer (C)

paritesh · Answer

Hi,
I think answer will be B. We can get 1,2 .zero is neither positive or negative and question is asking for positive values only.

PS
Any number to the left of zero on a number line; can be integer or non-integer. Note: The number zero is neither positive nor negative

Posted from my mobile device

Bunuel · Answer

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

P.S. This doubt is already addressed above. Please read the whole thread before posting. Thank you.

paritesh · Answer

Thanks,I got it I didn't read the question properly

Posted from my mobile device

pushkarajnjadhav · Answer

|4x - 3| < 6
remove the modulus
Case 1)
4x-3 <6
4x<9
x<9/4
x<2.25

Case 2)
-(4x-6)<6
4x-3>-6
4x>-3
x>-3/4
x>-0.75
Hence -0.75 < x < 2.25

Therefore only possible values for x are 0,1,2.

Hence Option C.

Kudos if it helps.

Madhavi1990 · Answer

Hi! Why is zero seen as an integer here? I understand 1,2 but zero isn't counted as an integer. Please correct my understanding. Thank you!

Bunuel · Answer

ZERO:

1. 0 is an integer.

2. 0 is an even integer. An even number is an   integer   that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

Brush up fundamentals before attempting questions:

ALL YOU NEED FOR QUANT ! ! ! 
 Ultimate GMAT Quantitative Megathread

Hope it helps.

AkshdeepS · Answer

Question: Number of possible values of x which are integer?

Given: |4x - 3| < 6

-6+3 < 4x < 6+3

-3/4 < x < 9/4

-0.75 < x < 2.25

values are 0, 1, 2 (Three integer values)

(C)

ScottTargetTestPrep · Answer

We can first solve when the expression (4x - 3) is positive:

4x - 3 < 6

4x < 9

x < 9/4 = 2 ¼

Now we can solve when the expression (4x - 3) is negative:

-(4x - 3) < 6

-4x + 3 < 6

-4x < 3

x > -3/4
Thus:

-3/4 < x < 2 1/4

So x can be any of 3 integer values: 0, 1, or 2.

Answer: C

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

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

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