2010001603
Level:
B
Assuming \(x\in (1;8)\),
simplify the following expression.
\[
2|x - 8|- 2|1 - x|
\]
\(- 4x + 18\)
\( 14\)
\(4x -18\)
\(- 14\)
Absolute value
2010001602
Level:
A
Simplifying \( \left|\sqrt3-3\right|-\left|2\sqrt3-2\right| \) we get:
\( -3\sqrt3+5 \)
\( -3\sqrt3+1 \)
\( \sqrt3+5 \)
\( \sqrt3+1 \)
2010001601
Level:
A
Evaluate the following expression.
\[
|2-5|+|2(-3)| - |(-3)(-1)|
\]
\(6\)
\(12\)
\(-12\)
\( -6\)
2000001605
Level:
B
Find all \(x\) such that the statement is true.
\[|-1-x|=1+x\]
\( x \in [ -1;\infty) \)
\( x \in [ 1;\infty) \)
\( x \in [ 0;\infty) \)
\( x \in \mathbb{R} \)
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.
\( x \in \mathbb{R}\)
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.
2000001602
Level:
B
Find all \(x\) such that the statement is true.
\[ |1-x| =1-x\]
\( x \in (-\infty;1] \)
\(x \in [ 1; \infty) \)
\( x \in[ -1; \infty) \)
\( x \in (-\infty;-1] \)
2000001601
Level:
B
Find all \(x\) such that the statement is true.
\[ |2x-1| =2x-1\]
\( x \in \left[ \frac{1}{2}; \infty\right) \)
\( x \in [ 2; \infty) \)
\( x \in [ -2; \infty) \)
\( x \in [ 5; \infty) \)
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.
\[|2-\pi| - |2\pi-2|\]
\(-\pi\)
\(3\pi\)
\(\pi+4\)
\(\pi\)