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
9000021704
Level:
B
Solve the following inequality.
\[
\frac{x + 1}
{4} -\frac{x + 2}
{3} > \frac{x + 3}
{6} -\frac{3x - 4}
{12}
\]
\(x\in \emptyset \)
\(x\in \mathbb{R}\)
\(x\in (-\infty ;29)\)
\(x\in \{0\}\)
9000021705
Level:
B
Solve the following inequality in the set of negative integers.
\[
\frac{3x - 4}
{2} -\frac{2x - 5}
{3} + \frac{3 - 4x}
{5} > 0
\]
\(x\in \{ - 7;-6;-5;-4;-3;-2;-1\}\)
\(x\in \emptyset \)
\(x\in [ - 8;0] \)
\(x\in \{ - 8;-7;-6;-5;-4;-3;-2;-1\}\)
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 \(\frac{2x+4}
{6} + \frac{x-3}
{3} \).
\(x\in [ 6;\infty )\)
\(x\in (6;\infty )\)
\(x\in (-\infty ;6)\)
\(x\in (-\infty ;6] \)
9000021710
Level:
B
Find the maximal integer \(x\)
which satisfies the following inequality.
\[
\frac{x + 6}
{3} -\frac{x - 1}
{2} < 2 - 0.2x
\]
\(- 16\)
\(- 15\)
\(- 14\)
\(14\)
9000021801
Level:
B
Solve the following system of inequalities.
\[\begin{aligned}
\frac{1}
{3}(2x + 5) &\geq 0.5\left (\frac{2 + 3x}
{2} + 2\right ) & &
\\0.2(3 - 2x) &\leq \frac{1}
{3}\left (\frac{4 - 2x}
{5} + 2\right ) & &
\end{aligned}\]
\(x\in \left [ -\frac{5}
{4};2\right ] \)
\(x\in [ 2;\infty )\)
\(x\in \left (-\infty ;-\frac{5}
{4}\right ] \)
\(x\in \emptyset \)
9000021802
Level:
B
Solve the following system of inequalities.
\[\begin{aligned}
15x - 2 &\geq 3x + 2 > 2x + 1 & &
\\10x + 1 & > 5x + 1\geq 6 - x & &
\end{aligned}\]
\(x\in \left [ \frac{5}
{6};\infty \right )\)
\(x\in [ - 1;\infty )\)
\(x\in \emptyset \)
\(x\in [ 2;\infty )\)
9000039002
Level:
B
Assuming \(x\in \mathbb{Z}\),
find the solution set of the following system.
\[
-3\leq 2(x + 2)\leq 6
\]
\(\{ - 3;-2;-1;0;1\}\)
\(\{ - 4;-2;-1;0;1\}\)
\(\{ - 3;-2;-1;0\}\)
\(\{0;1\}\)
9000039003
Level:
B
Assuming \(x\in \mathbb{R}\),
find the solution set of the following system.
\[
x + 2 > 2x + 3 > 3x + 5
\]
\((-\infty ;-2)\)
\((-2;+\infty )\)
\((-\infty ;-1)\)
\((-2;-1)\)
9100018007
Level:
B
Graph the solution of the following inequality.
\[
-x < 3
\]
