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12 Nov 2019, 03:49
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If \(|y| ≤ -4x\) and \(|3x - 4|= 2x + 6\). Which of the following could be the value of x?
A. -3
B. -1/2
C. -2/5
D. 1/3
E. 10
Are You Up For the Challenge: 700 Level Questions
A. -3
B. -1/2
C. -2/5
D. 1/3
E. 10
Are You Up For the Challenge: 700 Level Questions
12 Nov 2019, 07:18
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If \(|y| ≤ -4x\) and \(|3x - 4|= 2x + 6\). Which of the following could be the value of x?
A. -3
B. -1/2
C. -2/5 --> correct
D. 1/3
E. 10
Solution:
\(|y| ≤ -4x\)
=> \( -4x >= |y| >=0\)
=> -x>=0
=> x ≤ 0
So for |3x - 4|= 2x + 6
3x-4 can't be > 0 i.e. x can't be > 4/3, because x can't be > 0
So 3x - 4 ≤ 0
-(3x-4)=2x+6
=> 5x = -2
=> x = -2/5
A. -3
B. -1/2
C. -2/5 --> correct
D. 1/3
E. 10
Solution:
\(|y| ≤ -4x\)
=> \( -4x >= |y| >=0\)
=> -x>=0
=> x ≤ 0
So for |3x - 4|= 2x + 6
3x-4 can't be > 0 i.e. x can't be > 4/3, because x can't be > 0
So 3x - 4 ≤ 0
-(3x-4)=2x+6
=> 5x = -2
=> x = -2/5
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18 Nov 2019, 22:34
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\(|y|\) is an absolute value which means \(|y|\) cannot be negative
Therefore since \(|y|≤−4x\), \(x\) must be negative as \(|y|\) cannot be less than or equal to a negative value
Eliminate (D) and (E)
\(|3x−4|=2x+6\)
This means \(3x-4=2x+6\) or \(4-3x=2x+6\)
On solving we get, \(x=10\) or \(x=-\frac{2}{5}\)
Since we know that x must be negative, our answer is \(x=-\frac{2}{5}\)
Answer is (C)
Therefore since \(|y|≤−4x\), \(x\) must be negative as \(|y|\) cannot be less than or equal to a negative value
Eliminate (D) and (E)
\(|3x−4|=2x+6\)
This means \(3x-4=2x+6\) or \(4-3x=2x+6\)
On solving we get, \(x=10\) or \(x=-\frac{2}{5}\)
Since we know that x must be negative, our answer is \(x=-\frac{2}{5}\)
Answer is (C)
