2000001601
Level:
B
Find all \(x\) such that the statement is true.
\[ |2x-1| =2x-1\]
\( x \in \left[ \frac{1}{2}; \infty\right) \)
\( x \in [ 2; \infty) \)
\( x \in [ -2; \infty) \)
\( x \in [ 5; \infty) \)
Absolute value
2000001315
Level:
A
Evaluate the given expression.
\[\bigl\vert 1-\sqrt{2}\bigr\rvert+\bigl\lvert 3-\sqrt{2}\bigr\rvert\]
\(2\)
\(2\sqrt{2}\)
\(\sqrt{2}+1\)
\(2\sqrt{2}+4\)
2000001314
Level:
A
Evaluate the given expression.
\[|2-\pi| - |2\pi-2|\]
\(-\pi\)
\(3\pi\)
\(\pi+4\)
\(\pi\)
2000001313
Level:
A
Evaluate the given expression.
\[ |3-\pi| - |\pi -3|\]
\(0\)
\(\pi\)
\(2\pi\)
\(6\)
2000001312
Level:
A
Evaluate the given expression.
\[ 2\cdot \bigl\lvert\sqrt{2}+1\bigr\rvert-\bigl\lvert\sqrt{2}-2\bigr\rvert\]
\(3\sqrt{2}\)
\(0\)
\(\sqrt{2}\)
\(4\)
2000001311
Level:
A
Evaluate the given expression.
\[\bigl\lvert 1-\sqrt{2}\bigr\rvert-\bigl\lvert\sqrt{2}-1\bigr\rvert\]
\(0\)
\(1\)
\(\sqrt{2}\)
\(2\sqrt{2}\)
2000001310
Level:
A
Evaluate the given expression.
\[\biggl| 3-|1-6|\biggr| \cdot |2\cdot (-3)|\]
\(12\)
\(48\)
\(24\)
\(2\)
2000001309
Level:
A
Evaluate the given expression.
\[|-3\cdot (-2)-6|-|5\cdot(-1)-1|\]
\(-6\)
\(-7\)
\(8\)
\(6\)
2000001308
Level:
A
Evaluate the given expression.
\[\bigl\lvert-3-\sqrt{3}\bigr\rvert-\bigl\lvert\sqrt{3}-3\bigr\rvert\]
\(2\sqrt{3}\)
\(0\)
\(3\)
\(6\)
2000001307
Level:
A
Evaluate the given expression.
\[|7-4|-|-11-(-3)|\]
\(-5\)
\(-11\)
\(11\)
\(17\)