9000021704
Level:
B
Solve the following inequality.
\[
\frac{x + 1}
{4} -\frac{x + 2}
{3} > \frac{x + 3}
{6} -\frac{3x - 4}
{12}
\]
\(x\in \emptyset \)
\(x\in \mathbb{R}\)
\(x\in (-\infty ,29)\)
\(x\in \{0\}\)
B
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 \(\frac{2x+4}
{6} + \frac{x-3}
{3} \).
\(x\in [ 6,\infty )\)
\(x\in (6,\infty )\)
\(x\in (-\infty ,6)\)
\(x\in (-\infty ,6] \)
9000021703
Level:
B
Solve the following inequality.
\[
(x - 2)^{2}\geq (x + 1)(x - 5)
\]
\(x\in \mathbb{R}\)
\(x\in \emptyset \)
\(x\in \left (-\infty , \frac{9}
{8}\right ] \)
\(x\in \left [ \frac{9}
{8},\infty \right )\)
9000021803
Level:
B
Solve the following inequality.
\[
(3x - 1)(2 - 4x) < 0
\]
\(x\in \left (-\infty , \frac{1}
{3}\right )\cup \left (\frac{1}
{2},\infty \right )\)
\(x\in \left (\frac{1}
{3}, \frac{1}
{2}\right )\)
\(x\in \left (-\infty , \frac{1}
{2}\right )\)
\(x\in \left (\frac{1}
{3},\infty \right )\)
9000022301
Level:
B
Find the solution set of the quadratic inequality.
\[
x^{2} - 8x + 16\leq 0
\]
\(\{4\}\)
\(\emptyset \)
\(\mathbb{R}\setminus \{4\}\)
\(\mathbb{R}\)
\((-\infty ,4)\cup (4,\infty )\)
9000021804
Level:
B
Solve the following inequality.
\[
\frac{1}
{x - 3}\leq \frac{1}
{2 - x}
\]
\(x\in (-\infty ,2)\cup \left [ \frac{5}
{2},3\right )\)
\(x\in (-\infty ,2)\cup \left [ \frac{5}
{3},2\right ] \)
\(x\in \left (-\infty , \frac{5}
{2}\right ] \cup \left (3,\infty \right )\)
\(x\in \left [ \frac{5}
{2},\infty \right )\)
9000021710
Level:
B
Find the maximal integer \(x\)
which satisfies the following inequality.
\[
\frac{x + 6}
{3} -\frac{x - 1}
{2} < 2 - 0.2x
\]
\(- 16\)
\(- 15\)
\(- 14\)
\(14\)
9000021806
Level:
B
Solve the following inequality.
\[
\frac{1 - 3x}
{x + 2} \geq 0
\]
\(x\in \left (-2, \frac{1}
{3}\right ] \)
\(x\in \left [ \frac{1}
{3},\infty \right )\)
\(x\in \left (\frac{1}
{3},\infty \right )\)
\(x\in (-\infty ,-2)\cup \left [ \frac{1}
{3},\infty \right )\)
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 \(27\)