2000001201
Level:
B
Find all \(x \in \mathbb{R}\) such that the given relation is true.
\[ |x|=x\]
\( x \in [ 0,\infty) \)
\( x \in (-\infty,0] \)
\( x \in\mathbb{R}\)
No such \(x\) exists.
\( x \in \{0\} \)
Absolute Value
2000001202
Level:
B
Find all \(x \in \mathbb{R}\) such that the given relation is true.
\[ |x|=-x\]
\( x \in (-\infty,0] \)
\( x \in [ 0, \infty) \)
\(x \in \mathbb{R} \)
No such \(x\) exists.
\( x \in \{0\}\)
2000001203
Level:
B
Find all \(x \in \mathbb{R}\) such that the given relation is true.
\[ |-x|=-x\]
\( x \in (-\infty,0] \)
\( x \in [ 0, \infty) \)
\(x \in \mathbb{R} \)
No such \(x\) exists.
\( x \in \{0\}\)
2000001204
Level:
B
Find all \(x \in \mathbb{R}\) such that the given relation is true.
\[- |x|=-x\]
\( x \in [ 0, \infty) \)
\( x \in (-\infty,0] \)
\(x \in \mathbb{R} \)
No such \(x\) exists.
\( x \in \{0\}\)
2000001205
Level:
B
Find all \(x \in \mathbb{R}\) such that the given relation is true.
\[ -|x|=|-x|\]
\( x \in \{0\}\)
\( x \in [ 0, \infty) \)
\( x \in (-\infty,0] \)
\(x \in \mathbb{R} \)
No such \(x\) exists.
2000001601
Level:
B
Find all \(x\) such that the statement is true.
\[ |2x-1| =2x-1\]
\( x \in \left[ \frac{1}{2}, \infty\right) \)
\( x \in [ 2, \infty) \)
\( x \in [ -2, \infty) \)
\( x \in [ 5, \infty) \)
2000001602
Level:
B
Find all \(x\) such that the statement is true.
\[ |1-x| =1-x\]
\( x \in (-\infty,1] \)
\(x \in [ 1, \infty) \)
\( x \in[ -1, \infty) \)
\( x \in (-\infty,-1] \)
2000001603
Level:
B
Find all \(x\) such that the statement is true.
\[|-1-x| = -1-x\]
\( x \in (-\infty,-1 ]\)
\( x \in (-\infty,1 ]\)
\(x \in [ 1,\infty) \)
No such \(x\) exists.
2000001604
Level:
B
Find all \(x\) such that the statement is true.
\[|3-2x|=-3+2x\]
\( x \in \left[ \frac{3}{2},\infty\right) \)
\( x \in [ 2,\infty) \)
No such \(x\) exists.
\( x \in \mathbb{R}\)
2000001605
Level:
B
Find all \(x\) such that the statement is true.
\[|-1-x|=1+x\]
\( x \in [ -1,\infty) \)
\( x \in [ 1,\infty) \)
\( x \in [ 0,\infty) \)
\( x \in \mathbb{R} \)