9000021702
Level:
B
Find the positive integer solutions of the following inequality.
\[
\frac{1 + x}
{3} -\frac{8 - 3x}
{2} < \frac{3x}
{2} - 2
\]
\(x\in \{1;2;3;4\}\)
\(x\in \mathbb{N}\)
\(x\in \{1;2;3;4;5\}\)
\(x\in [ 1;5] \)
Linear Equations and Inequalities
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 \(\frac{2x+4}
{6} + \frac{x-3}
{3} \).
\(x\in [ 6;\infty )\)
\(x\in (6;\infty )\)
\(x\in (-\infty ;6)\)
\(x\in (-\infty ;6] \)
9000021701
Level:
B
Assume \(x\in [ - 2;2] \)
and solve the following inequality.
\[
10 + 7x\leq 5 - 3x
\]
\(x\in \left [ -2;-\frac{1}
{2}\right ] \)
\(x\in \left (-\infty ;-\frac{1}
{2}\right ] \)
\(x\in \left [ -\frac{1}
{2};2\right ] \)
\(x\in [ - 2;2] \)
9000018106
Level:
B
Find the set of all the positive integers
\(x\) for which the
expression \(\frac{3x-7}
{14} \) is
smaller than \(\frac{7-2x}
{7} \).
\(\left \{1;2\right \}\)
\(\left \{1;2;3;4\right \}\)
\(\left \{1;2;3\right \}\)
\(\left \{1\right \}\)
9000018107
Level:
B
Solve the following inequality in the set of negative integers.
\[
\frac{x}
{6} + \frac{3x - 2}
{2} > -5
\]
\(x\in \left \{-2;-1\right \}\)
\(x\in \left \{-3;-2;-1\right \}\)
\(x\in \left \{-3;-2\right \}\)
\(x\in \left \{-1\right \}\)
9000018110
Level:
C
Consider a coil composed from a ferrite core and a wire winding. The mass of the
core is \(2\, \mathrm{kg}\).
The material for the wire is such that the mass of the wire of the length
\(30\, \mathrm{m}\) is bigger than the mass
of the wire of the length \(10\, \mathrm{m}\)
together with the ferrite core. In the following list identify a possible mass of one
meter of the wire.
\(110\, \mathrm{g}\)
\(100\, \mathrm{g}\)
\(0.01\, \mathrm{kg}\)
\(0.09\, \mathrm{kg}\)
9000018101
Level:
B
Solve the following inequality:
\[
7 -\left (4x - 1\right ) < 3\left (x + 4\right )
\]
\(x\in \left (-\frac{4}
{7};\infty \right )\)
\(x\in \left (-\infty ; \frac{4}
{7}\right )\)
\(x\in \left (\frac{4}
{7};\infty \right )\)
\(x\in \left (-\infty ;-\frac{4}
{7}\right )\)
9000018102
Level:
B
Solve the following inequality:
\[
\left (5 + 2x\right )\cdot \left (-3\right ) + 16 < 20 - 6x
\]
\(x\in \left (-\infty ;\infty \right )\)
\(x\in \left (-\infty ;2\right )\)
\(x\in \emptyset \)
\(x\in \left (2;\infty \right )\)
9000018004
Level:
B
Find the maximal integer which satisfies the following inequality:
\[
2x - 5 < 4 - x
\]
\(2\)
\(- 3\)
\(- 2\)
\(3\)
9000018001
Level:
B
Solve the following inequality.
\[
-3x > 6
\]
\(x\in \left (-\infty ;-2\right )\)
\(x\in \left (-\infty ;-2\right ] \)
\(x\in \left (-2;\infty \right )\)
\(x\in \left [ -2;\infty \right )\)