2010015902
Level:
B
Find the solution set of the following inequality.
\[
\frac{x+3}
{1-2x} \geq 0
\]
\(\left[ -3; \frac12 \right) \)
\( [ -3;\infty )\)
\( \left(-\infty;\frac12\right)\)
\( (-\infty;-3 ] \cup \left(\frac12;\infty\right)\)
Rational equations and inequalities
2010015901
Level:
B
Find all real values of \(x\) for which the fraction \(\frac{2}{x+3}\) is negative.
\( x < -3\)
\( x>-3\)
\( x< 3\)
\(x>3\)
2010012107
Level:
A
Find the solution set of the following equation.
\[ \frac2{5x^2-20}=0 \]
\(\emptyset\)
\(\left \{2\right \}\)
\( \left \{-2;2\right \}\)
\(\left \{-2\right \}\)
2010012106
Level:
A
Find the solution set of the following equation.
\[ \frac{4x^2-16}{x-2}=0 \]
\(\left \{-2\right \}\)
\( \left \{-2;2\right \}\)
\(\left \{2\right \}\)
\(\emptyset\)
2010012105
Level:
A
Find the solution set of the following equation.
\[ \frac{x^2-6x+9}{x-3}=0 \]
\(\emptyset\)
\(\left \{3\right \}\)
\( \left \{-3;3\right \}\)
\(\left \{-3\right \}\)
2010012104
Level:
A
Given graphs of the functions \( f(x)= x^2+x-6 \) and \( g(x) = x-2 \), find the domain of the equation \( \frac{x-2}{x^2+x-6}=1 \).
\(\mathbb{R}\setminus \left \{-3;2\right \}\)
\(\mathbb{R}\setminus \left \{-2;2\right \}\)
\(\mathbb{R}\setminus \left \{-3;-2;2\right \}\)
\(\mathbb{R}\setminus \left \{0\right \}\)
2010012103
Level:
A
Find the domain of the expression.
\[
\frac{x^2-x-12}{3x^2+17x-6}
\]
\(\mathbb{R}\setminus \left \{-6;\frac{1}
{3}\right \}\)
\(\mathbb{R}\setminus \left \{-\frac{1}
{3};6\right \}\)
\(\left(-\frac13;6\right)\)
\(\left(-6;\frac13\right)\)
2010012102
Level:
A
Find the solution set of the following equation.
\[
\frac{9x +3}
{3x + 1} = 3
\]
\(\mathbb{R}\setminus \left \{-\frac{1}
{3}\right \}\)
\(\mathbb{R}\)
\(\{ 3\}\)
\(\emptyset\)
2010012101
Level:
A
Find the solution set of the following equation.
\[
\frac{2}
{9x^2-9} = 0
\]
\(\emptyset\)
\(\{ -1;1\}\)
\(\{ - 2\}\)
\(\{ 1\}\)
2110011904
Level:
C
Identify the picture that shows the correct solution set of the following inequality. In each picture, the set of points corresponding to the solution set is marked in red.
\[
\frac{2}
{x}\geq x-1
\]
