1003124205
Level:
B
Assuming \( x\in(4;7) \), the expression \( |x-4|-|x-7| \) can be written in the form:
\( 2x-11 \)
\( -2x+11 \)
\( 3 \)
\( -11 \)
Absolute value
1003124204
Level:
B
Let \( x\neq0 \). Complete the following sentence to get a true statement. The solution set of the inequality \( \frac{|x|}x>2 \)
does not contain any integer.
contains \( 2 \) integers.
contains only natural numbers.
contains infinitely many integers.
1003124203
Level:
B
Assuming \( x < 0 \), the expression \( \bigl| |x|+2 \bigr| \) is equal to:
\( -x+2 \)
\( x+2 \)
\( -x-2 \)
\( x-2 \)
1003124202
Level:
A
The value of \( |2-6|-|-1+3| \) is equal to:
\( 2 \)
\( -6 \)
\( 0 \)
\( 8 \)
1003124201
Level:
B
Which equation describes real numbers \( x \) that are equidistant from the numbers \( 6 \) and \( -3 \) on the number line?
\( |x-6|=|x+3| \)
\( |x+6|=|x+3| \)
\( |x-6|=|x-3| \)
\( |x+6|=|x-3| \)
1003049203
Level:
C
Identify which of the statements is false.
\( \forall a\text{, }b\in\mathbb{R}\colon |a+b|=|a|+|b| \)
\( \forall a\text{, }b\in\mathbb{R}\colon |a\cdot b|=|a|\cdot|b| \)
\( \forall a\in\mathbb{R}\text{, }b\in\mathbb{R}\setminus\{0\}\colon|\frac ab|=\frac{|a|}{|b|} \)
\( a\in\mathbb{R}\colon |a|=|-a| \)
9000081406
Level:
C
For \(x\in \mathbb{R}\) find the correct
relationship between \(|x|\)
and \(|- x|\).
\(|x| = |- x|\)
\(|x| > |- x|\)
\(|x| < |- x|\)
None of them. The answer depends on the particular value of
\(x\).
9000081407
Level:
C
For \(x,y\in \mathbb{R}\) find the correct
relationship between \(|x - y|\)
and \(|y - x|\).
\(|x - y| = |y - x|\)
\(|x - y| > |y - x|\)
\(|x - y| < |y - x|\)
None of them. The answer depends on the particular values of
\(x\),
\(y\).
9000081408
Level:
B
For \(x\in \mathbb{R}^{-}\) consider
expressions \(|x|\),
\(|- x|\),
\(-|x|\) and
\(- x\).
Which of these attains only negative values?
\(-|x|\)
\(|x|\)
\(|- x|\)
\(- x\)
9000081409
Level:
C
Among expressions \(1 + |x|\),
\(|1 + x|\),
\(1 -|x|\) and
\(|1 - x|\) on the
set \(x\in (-\infty ;-1)\)
find the expression which has smaller values than the other expressions from this list.
\(1 -|x|\)
\(1 + |x|\)
\(|1 + x|\)
\(|1 - x|\)
None of them.