2010008505
Level:
C
Give the solution set of the equation \( \left| |2+x|-|x-4| \right|=6\).
\( (-\infty;-2] \cup [ 4 ;+\infty) \)
\( (-\infty;-4] \cup [ 2 ;+\infty) \)
\( [ -2 ;+\infty) \)
\( [ 4 ;+\infty) \)
Absolute value equations and inequalities
2010008504
Level:
B
Give the number which satisfies the equation \( |x+2|-1=x+3\).
\(-3\)
\( -2 \)
\( 0 \)
\( 1 \)
2010008503
Level:
A
Choose the equation which has only one solution.
\( 5-|2x+2|-1=4 \)
\( 5-|2x+2|+1=5 \)
\( -|2x+2|+3=4 \)
\( -|2x+2|+1=0 \)
2010008502
Level:
C
Find all \( t\in\mathbb{R} \), such that the following equation with the variable \( x \) has more than two solutions.
\[ \Bigl| 1-|2-x|\Bigr|+1=t \]
\( t\in(1;2 ] \)
\( t\in\{2\} \)
\( t\in(2;\infty) \)
\( t \in \emptyset \)
2010008501
Level:
B
Find all \( t\in\mathbb{R} \), such that the following equation with the variable \( x \) has exactly two solutions.
\[ |x+2|+3=t-1 \]
\( t\in(4;\infty) \)
\( t\in(-2;\infty) \)
\( t\in\{4\} \)
\( \mathbb{R}\)
2000002205
Level:
A
Identify the solution set of the following inequality.
\[
|7x+1|+1>0
\]
\( \mathbb{R} \)
\( \emptyset \)
\( \mathbb{R} \setminus \left\{\frac{1}{7}\right\} \)
\( \mathbb{R} \setminus \left\{-\frac{1}{7}\right\} \)
2000002204
Level:
A
Identify the solution set of the following inequality.
\[
-|2x-100|< 0
\]
\( \mathbb{R} \setminus \{50\} \)
\( \mathbb{R} \)
\( \mathbb{R} \setminus \{-50\} \)
\( \{50\} \)
2000002203
Level:
C
Identify the solution set of the following inequality.
\[
|x + 2| + |x + 3| \leq 0
\]
\( \emptyset \)
\( \mathbb{R} \)
\( \mathbb{R} \setminus \{-3;-2\} \)
\( \{-3;-2\} \)
2000002202
Level:
A
Identify the solution set of the following inequality.
\[
|x-25| \leq 0
\]
\( \{25\} \)
\( \emptyset \)
\( \mathbb{R} \setminus \{25\} \)
\( (-\infty;-25) \)
2000002201
Level:
A
Identify the solution set of the following inequality.
\[
|2x+5|>0
\]
\( \mathbb{R} \setminus \{-2.5\} \)
\( \emptyset \)
\( (-2.5; \infty) \)
\( (-\infty;-2.5 ) \)