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What values of x will satisfy the following inequality? |x-3|> |x|-3 26 Oct 2019, 10:24
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A
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75% (hard)

Question Stats:

57% (02:04) correct 43% (02:00) wrong based on 336 sessions

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What values of x will satisfy the following inequality?
\(|x-3|> |x|-3\)

A. x∈ (-∞, 3)
B. x∈ (-3, 3)
C. x∈ (-∞, -3)
D. x∈ (∞, 3)
E. x∈ (-∞, -3) ∪ (3, ∞)
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A
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satya2029
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What values of x will satisfy the following inequality? |x-3|> |x|-3 26 Oct 2019, 11:47
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Asad
What values of x will satisfy the following inequality?
\(|x-3|> |x|-3\)

A. x∈ (-∞, 3)
B. x∈ (-3, 3)
C. x∈ (-∞, -3)
D. x∈ (∞, 3)
E. x∈ (-∞, -3) ∪ (3, ∞)
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Posted from my mobile device

Kindly correct choice D
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TestPrepUnlimited
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What values of x will satisfy the following inequality? |x-3|> |x|-3 29 Dec 2020, 17:06
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TheUltimateWinner
What values of x will satisfy the following inequality?
\(|x-3|> |x|-3\)

A. x∈ (-∞, 3)
B. x∈ (-3, 3)
C. x∈ (-∞, -3)
D. x∈ (∞, 3)
E. x∈ (-∞, -3) ∪ (3, ∞)
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We can pick a value from each interval and see which of them satisfy. The answers all belong to one or more of the following intervals:
(1) (-∞, -3). Try -5, we get \(|-8| > 5 - 3\) and \(8 > 2\) which is true.
(2) (-3, 3). Try 0, we get \(|-3| > -3\) and \(3 > -3\) which is true.
(3) (3, ∞). Try 5, we get \(|2| > 5 - 3\) and \(2 > 2\) which is false.

Thus both (1) and (2) are correct, combining their intervals we get (-∞, 3) which is A

Ans: A
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What values of x will satisfy the following inequality? |x-3|> |x|-3 27 Mar 2021, 10:46
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TheUltimateWinner
What values of x will satisfy the following inequality?
\(|x-3|> |x|-3\)

A. x∈ (-∞, 3)
B. x∈ (-3, 3)
C. x∈ (-∞, -3)
D. x∈ (∞, 3)
E. x∈ (-∞, -3) ∪ (3, ∞)
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Any other solution to this problem?

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What values of x will satisfy the following inequality? |x-3|> |x|-3 30 Mar 2021, 03:18
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Can anyone solve this inequality algebraically

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What values of x will satisfy the following inequality? |x-3|> |x|-3 06 Apr 2021, 21:12
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This is the way I solved it algebraically:


[X - 3] > [X] - 3


The 2 Critical Boundaries over which the value inside each Modulus will change sign (“critical points”) will be:

X = 0 and + 3

So we need to open Each Modulus under 3 Assumed Scenarios:


Range 1: X >/= +3

X - 3 > X - 3

0 > 0 ——- false

No value that equals +3 or greater will satisfy the inequality


Range 2: 0 </= X < +3

-(X - 3) > X - 3

-X + 3 > X - 3

6 > 2X

X < 3

For all values from: 0 </= X < 3

The inequality will be satisfied. (Note: +3 does not work)


Range 3: X < 0

-(X - 3) > -(X) - 3

-X + 3 > -X - 3

+ 3 > -3

True——-test any value from 0 to negative infinite and you will see that the range will be satisfied.


Answer: X < 3

Any value in this range will satisfy the inequality


aka14
Can anyone solve this inequality algebraically

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What values of x will satisfy the following inequality? |x-3|> |x|-3 14 Mar 2024, 22:34
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Asked: What values of x will satisfy the following inequality?\(|x-3|> |x|-3\)
Case 1: x<0
3 - x > -x - 3
3 > -3 
ALWAYS TRUE

Case 2: 0<=x<=3
3-x > x-3
x < 3
ALWAYS TRUE

Case 3: x>3
x-3 > x -3
Not feasible since x -3 = x - 3

x∈ (-∞, 3)

IMO A
­
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What values of x will satisfy the following inequality? |x-3|> |x|-3 06 Jul 2024, 07:36
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Kinshook
Asked: What values of x will satisfy the following inequality?\(|x-3|> |x|-3\)
Case 1: x<0
3 - x > -x - 3
3 > -3 
ALWAYS TRUE

Case 2: 0<=x<=3
3-x > x-3
x < 3
ALWAYS TRUE

Case 3: x>3
x-3 > x -3
Not feasible since x -3 = x - 3

x∈ (-∞, 3)

IMO A
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­Hi, how do we decide the critical points in this equation?
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What values of x will satisfy the following inequality? |x-3|> |x|-3 08 Jul 2024, 06:08
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Kinshook
Asked: What values of x will satisfy the following inequality?\(|x-3|> |x|-3\)
Case 1: x<0
3 - x > -x - 3
3 > -3 
ALWAYS TRUE

Case 2: 0<=x<=3
3-x > x-3
x < 3
ALWAYS TRUE

Case 3: x>3
x-3 > x -3
Not feasible since x -3 = x - 3

x∈ (-∞, 3)

IMO A
­
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At x=3 both sides of equation becomes equal to zero and hence the the inequality fails

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What values of x will satisfy the following inequality? |x-3|> |x|-3 21 Aug 2025, 08:21
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