9000018004
Level:
B
Find the maximal integer which satisfies the following inequality:
\[
2x - 5 < 4 - x
\]
\(2\)
\(- 3\)
\(- 2\)
\(3\)
Linear Equations and Inequalities
9000018006
Level:
B
Assuming negative integer \(x\),
solve the following inequality:
\[
x - 2 > 1 - x - 8
\]
\(x\in \left \{-2,-1\right \}\)
\(x\in \left \{-3,-2,-1\right \}\)
\(x\in \left \{-3,-2\right \}\)
\(x\in \left \{-1\right \}\)
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:
\[
\left (5 + 2x\right )\cdot \left (-3\right ) + 16 < 20 - 6x
\]
\(x\in \left (-\infty ,\infty \right )\)
\(x\in \left (-\infty ,2\right )\)
\(x\in \emptyset \)
\(x\in \left (2,\infty \right )\)
9000018103
Level:
B
Solve the following inequality assuming positive integer
\(x\).
\[
1\frac{1}
{3}\leq -\frac{x - 4}
{2}
\]
\(x\in \left \{1\right \}\)
\(x\in \left \{0,1\right \}\)
\(x\in \left (0, \frac{4}
{3}\right ] \)
\(x\in \emptyset \)
9000018104
Level:
B
Find the maximal integer which solves the following inequality.
\[
1 - 3x > 3\left (4 - x\right ) + 2x
\]
\(- 6\)
\(- 5\)
\(- 3\)
\(- 2\)
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.
\[
\frac{x}
{6} + \frac{3x - 2}
{2} > -5
\]
\(x\in \left \{-2,-1\right \}\)
\(x\in \left \{-3,-2,-1\right \}\)
\(x\in \left \{-3,-2\right \}\)
\(x\in \left \{-1\right \}\)
9000021701
Level:
B
Assume \(x\in [ - 2,2] \)
and solve the following inequality.
\[
10 + 7x\leq 5 - 3x
\]
\(x\in \left [ -2,-\frac{1}
{2}\right ] \)
\(x\in \left (-\infty ,-\frac{1}
{2}\right ] \)
\(x\in \left [ -\frac{1}
{2},2\right ] \)
\(x\in [ - 2,2] \)
9000021702
Level:
B
Find the positive integer solutions of the following inequality.
\[
\frac{1 + x}
{3} -\frac{8 - 3x}
{2} < \frac{3x}
{2} - 2
\]
\(x\in \{1,2,3,4\}\)
\(x\in \mathbb{N}\)
\(x\in \{1,2,3,4,5\}\)
\(x\in [ 1,5] \)