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# How many integer values are there for x such that |2x-3| < 3​

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How many integer values are there for x such that |2x-3| < 3​  [#permalink]

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14 Feb 2020, 23:49
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What is the sum of integer values of x such that |2x-3| < 3​?

a. One ​

b. Two​

c. Three​

d. Four​

e. Five​

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How many integer values are there for x such that |2x-3| < 3​  [#permalink]

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15 Feb 2020, 08:42
Top Contributor
1
kapil1 wrote:
What is the sum of integer values of x such that |2x - 3| < 3​?

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
----------------------------

Given: |2x - 3| < 3
From Rule #1, we can conclude that: -3 < 2x - 3 < 3
Add 3 to all sides of the inequality to get: 0 < 2x < 6
Divide all sides by 2 to get: 0 < x < 3

Since we're looking for INTEGER values of x, we see that x can equal 1 or 2
So the SUM = 1 + 2 = 3

Cheers,
Brent
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How many integer values are there for x such that |2x-3| < 3​  [#permalink]

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16 Feb 2020, 12:17
kapil1 wrote:
What is the sum of integer values of x such that |2x-3| < 3​?

a. One ​

b. Two​

c. Three​

d. Four​

e. Five​

$$|2x-3| < 3​$$

$$-3 < 2x - 3 < 3$$

$$0 < 2x < 6$$

$$0 < x < 3$$

Thus we can only take x = 1 and x = 2. The sum of solutions is 3.

Ans: C

If we had something like $$-6 < x < 9$$ however, note that the negative and positive integer x solutions cancel out so we only need to pay attention to x = 6, 7, and 8 in this case. The sum would be 7 * 3 = 21.
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How many integer values are there for x such that |2x-3| < 3​  [#permalink]

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Updated on: 06 Jun 2020, 22:34
kapil1 wrote:
What is the sum of integer values of x such that |2x-3| < 3​?

a. One ​

b. Two​

c. Three​

d. Four​

e. Five​

Asked: What is the sum of integer values of x such that |2x-3| < 3​?

|2x - 3| < 3

Case 1: x > 1.5
2x - 3 < 3
2x < 6
x < 3
x = 2

Case 2: x < 1.5
3 - 2x < 3
x > 0
x = 1

x = { 1,2};
Sum of integer solutions of x = 1+ 2 = 3

IMO C
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Email: kinshook.chaturvedi@gmail.com

Originally posted by Kinshook on 06 Jun 2020, 22:32.
Last edited by Kinshook on 06 Jun 2020, 22:34, edited 1 time in total.
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Re: How many integer values are there for x such that |2x-3| < 3​  [#permalink]

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06 Jun 2020, 22:33
kapil1 wrote:
What is the sum of integer values of x such that |2x-3| < 3​?

a. One ​

b. Two​

c. Three​

d. Four​

e. Five​

Asked: What is the sum of integer values of x such that |2x-3| < 3​?

|2x - 3| < 3

Case 1: x > 1.5
2x - 3 < 3
2x < 6
x < 3
x = 2

Case 2: x < 1.5
3 - 2x < 3
x > 0
x = 1

x = { 1,2};
Sum of integer solutions of x = 1 + 2 = 3

IMO C
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Email: kinshook.chaturvedi@gmail.com
Re: How many integer values are there for x such that |2x-3| < 3​   [#permalink] 06 Jun 2020, 22:33