1003163001
Level:
B
Find all \( t \), \( t\in\mathbb{R} \), such that the following equation with the variable \( x \) has exactly two solutions.
\[ |x|+t=-3 \]
\( t\in(-\infty;-3) \)
\( t\in\{-3\} \)
\( t\in(-3;\infty) \)
\( t\in\{-3;3\} \)
Absolute value equations and inequalities
1003177805
Level:
C
Let \( x\in\mathbb{Z} \). Find the sum of all the solutions of the given inequality.
\[ \Bigl| \bigl| |x+1|+1 \bigr|+1\Bigr| \leq 3 \]
\( -3 \)
\( -2 \)
\( -4 \)
\( 0 \)
1003177804
Level:
C
Choose the solution set of the given inequality.
\[ \left| |x-5|+2\right| > 3 \]
\( (-\infty;4)\cup(6;\infty) \)
\( (-\infty;-4)\cup(6;\infty) \)
\( (6;\infty) \)
\( (-\infty;-5)\cup(6;\infty) \)
1003187312
Level:
A
The solution set of an inequality in interval notation is \( (-\infty;-12]\cup[12;\infty) \). Find this inequality.
\( |x| \geq 12 \)
\( |x|\leq 12 \)
\( |x| > 12 \)
\( |x| < 12 \)
1103187311
Level:
A
Which graph shows the solution set of the inequality \( |x-3| \geq 1 \)?
1103187310
Level:
A
The solution set of an inequality is graphed on the number line. Determine this inequality.
\( |x+2| \leq 3 \)
\( |x-2| \leq 3 \)
\( |x-3| \leq 2 \)
\( |x+3| \leq 2 \)
1003187309
Level:
B
Give the number which satisfies the equation \( |6x+4|+4x=0 \).
\( x=-2 \)
\( x=1 \)
\( x=2 \)
\( x=-1 \)
1003187308
Level:
A
Choose the equation which has only one solution.
\( 4+|2x-6|=4 \)
\( 2-|x-3|=1 \)
\( |x-3|+2=-1 \)
\( 2-|x-3|=-2 \)
1003187307
Level:
A
The solutions of the equation \( |14-4x|=4 \) are:
the numbers differing by \( 2 \).
the numbers differing by \( 1 \).
integers.
opposite numbers.
1003187306
Level:
A
Let \( |2x+6|-4=0 \). Choose the correct statement.
The equation has two solutions.
Any real value of \( x \) is a solution.
The equation has just one solution.
The equation has no solution.