9000021703
Level:
B
Solve the following inequality.
\[
(x - 2)^{2}\geq (x + 1)(x - 5)
\]
\(x\in \mathbb{R}\)
\(x\in \emptyset \)
\(x\in \left (-\infty ; \frac{9}
{8}\right ] \)
\(x\in \left [ \frac{9}
{8};\infty \right )\)
B
9000021702
Level:
B
Find the positive integer solutions of the following inequality.
\[
\frac{1 + x}
{3} -\frac{8 - 3x}
{2} < \frac{3x}
{2} - 2
\]
\(x\in \{1;2;3;4\}\)
\(x\in \mathbb{N}\)
\(x\in \{1;2;3;4;5\}\)
\(x\in [ 1;5] \)
9000021803
Level:
B
Solve the following inequality.
\[
(3x - 1)(2 - 4x) < 0
\]
\(x\in \left (-\infty ; \frac{1}
{3}\right )\cup \left (\frac{1}
{2};\infty \right )\)
\(x\in \left (\frac{1}
{3}; \frac{1}
{2}\right )\)
\(x\in \left (-\infty ; \frac{1}
{2}\right )\)
\(x\in \left (\frac{1}
{3};\infty \right )\)
9000021709
Level:
B
Find all the values of \(x\)
for which the expression \(\frac{x+5}
{4} -\frac{7-3x}
{12} \)
is not bigger than \(\frac{2x+4}
{6} + \frac{x-3}
{3} \).
\(x\in [ 6;\infty )\)
\(x\in (6;\infty )\)
\(x\in (-\infty ;6)\)
\(x\in (-\infty ;6] \)
9000021804
Level:
B
Solve the following inequality.
\[
\frac{1}
{x - 3}\leq \frac{1}
{2 - x}
\]
\(x\in (-\infty ;2)\cup \left [ \frac{5}
{2};3\right )\)
\(x\in (-\infty ;2)\cup \left [ \frac{5}
{3};2\right ] \)
\(x\in \left (-\infty ; \frac{5}
{2}\right ] \cup \left (3;\infty \right )\)
\(x\in \left [ \frac{5}
{2};\infty \right )\)
9000021701
Level:
B
Assume \(x\in [ - 2;2] \)
and solve the following inequality.
\[
10 + 7x\leq 5 - 3x
\]
\(x\in \left [ -2;-\frac{1}
{2}\right ] \)
\(x\in \left (-\infty ;-\frac{1}
{2}\right ] \)
\(x\in \left [ -\frac{1}
{2};2\right ] \)
\(x\in [ - 2;2] \)
9000021809
Level:
B
Solve the following inequality.
\[
\frac{2x + 4}
{x - 1} < 1
\]
\(x\in (-5;1)\)
\(x\in (-\infty ;5)\)
\(x\in (1;\infty )\)
\(x\in (-\infty ;-3)\cup (1;\infty )\)
9000020909
Level:
B
The sum of squares of two consecutive integers is
\(1201\).
Identify these integers.
\(24\)
and \(25\)
\(23\)
and \(24\)
\(25\)
and \(26\)
\(26\)
and \(27\)
9000021810
Level:
B
Find all the values of \(x\)
for which the following expression takes on values smaller than or equal to
\(1\).
\[
\frac{x + 1}
{x - 1} - \frac{1}
{x + 1}
\]
\(x\in (-\infty ;-3] \cup (-1;1)\)
\(x\in (-\infty ;-3] \)
\(x\in (-\infty ;-1)\cup (-1;1)\cup (1;\infty )\)
\(x\in [ - 3;-1)\)
9000021808
Level:
B
Find the domain of the following function.
\[
f(x) = \sqrt{\frac{(x - 3)(x + 2)}
{(1 - x)(3 - x)}}
\]
\(\mathop{\mathrm{Dom}}(f) = (-\infty ;-2] \cup (1;3)\cup (3;\infty )\)
\(\mathop{\mathrm{Dom}}(f) = (-\infty ;-2)\cup (1;3)\)
\(\mathop{\mathrm{Dom}}(f) = (-\infty ;-2] \cup (1;\infty )\)
\(\mathop{\mathrm{Dom}}(f) =[ -2;1)\cup (3;\infty )\)