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25 Apr 2024, 01:30
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B
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26%
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If \(|x + 2| = |x|\), how many values of \(x\) satisfy this equation?
A. 0
B. 1
C. 2
D. 3
E. 4
A. 0
B. 1
C. 2
D. 3
E. 4
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04 May 2024, 18:45
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Official Solution:
If \(|x + 2| = |x|\), how many values of \(x\) satisfy this equation?
A. 0
B. 1
C. 2
D. 3
E. 4
Square to get rid of the absolute value (note here that we can safely do that since both sides of the equation are non-negative):
\(x^2+4x+4=x^2\);
\(x=-1\).
Therefore, only one value of \(x\) satisfies the given equation.
Answer: B
If \(|x + 2| = |x|\), how many values of \(x\) satisfy this equation?
A. 0
B. 1
C. 2
D. 3
E. 4
Square to get rid of the absolute value (note here that we can safely do that since both sides of the equation are non-negative):
\(x^2+4x+4=x^2\);
\(x=-1\).
Therefore, only one value of \(x\) satisfies the given equation.
Answer: B
General Discussion
25 Apr 2024, 01:59
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Bunuel
If \(|x + 2| = |x|\), how many values of \(x\) satisfy this equation?
A. 0
B. 1
C. 2
D. 3
E. 4
\(|x + 2| = |x|\)A. 0
B. 1
C. 2
D. 3
E. 4
Squaring both sides of the equation
\(x^2 + 4x + 4 = x^2\)
\(4x = -4\)
\(x = -1\)
Hence, only for one value of \(x\), \(|x + 2| = |x|\)
Option B
