2000001201 Level: BFind 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.\( x \in \{0\} \)
2000001202 Level: BFind 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: BFind 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: BFind 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: BFind 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: BFind 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: BFind 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: BFind 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: BFind 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: BFind all \(x\) such that the statement is true. \[|-1-x|=1+x\]\( x \in [ -1;\infty) \)\( x \in [ 1;\infty) \)\( x \in [ 0;\infty) \)\( x \in \mathbb{R} \)