2010011903
Level:
C
Find the solution set of the given inequality.
\[ \frac{x+1}{|3-x|} < 1 \]
\( (-\infty;1) \)
\( [ -1;3)\)
\([ 1,3)\cup(3;\infty) \)
\((-\infty;-1 ]\)
Rational equations and inequalities
2010011902
Level:
C
Find the solution set of the given inequality.
\[ \frac{|3x+4|}{2-x} > 1 \]
\( (-\infty;-3)\cup\left(-\frac12;2\right) \)
\( (2;\infty)\)
\( (-\infty;-3)\cup(2;\infty) \)
\((-3;-\frac12 ]\)
2010011901
Level:
C
Find the solution set of the given inequality.
\[ \frac{|4x+1|}{x(x+3)} \leq 0 \]
\( (-3;0) \)
\( [ -3;0 ] \)
\( (-\infty;-3)\cup(0;\infty) \)
\(\left(-3;-\frac14 \right]\)
2000005308
Level:
C
Use the graphs of the functions \(f(x)=x-3\) and \(g(x)=4-x\) to find the solution set of the following inequality.
\[\frac{x-3}{4-x} < 0\]
\( x \in (-\infty;3) \cup (4;+\infty) \)
\( x \in (3;4) \)
\( x \in (-\infty;3) \)
\( x \in (-\infty;0) \)
2000005307
Level:
C
Use the graphs of the functions \(f(x)=x+3\) and \(g(x)=x-1\) to find the solution set of the following inequality.
\[\frac{x+3}{x-1} \leq 0\]
\( x \in [ -3;1) \)
\( x \in [ -3;1] \)
\( x \in (1;+\infty) \)
\( x \in (-1;+\infty) \)
2000005306
Level:
C
Use the graphs of the functions \(f(x)=x^2-4\) and \(g(x)=x+2\) to find the solution set of the following inequality.
\[\frac{x^2-4}{x+2} \geq 0\]
\( x \in [ 2;+\infty) \)
\( x \in ( 2;+\infty) \)
\( x \in (-\infty;-2) \cup ( 2;+\infty) \)
\( x \in (-\infty;-2] \cup [ 2;+\infty) \)
2000005305
Level:
B
Find all real values of \(x\) such that the fraction \( \frac{7}{x^2+1} \) is negative.
\( \emptyset \)
\( x \in \mathbb{R} \)
\( x \in (-1;+\infty) \)
\( x \in \mathbb{R}\setminus \{ \pm 1\}\)
2000005304
Level:
B
Find all real values of \( x\) such that the fraction \( \frac{5}{x^2}\) is positive.
\( x \in \mathbb{R}\setminus \{0\}\)
\( x \in \mathbb{R}\)
\( x \in (0;+\infty)\)
\( x \in [ 0;+\infty)\)
2000005303
Level:
C
Use the graphs of the functions \( f(x)=x^2-5x+4\) and \(g(x)=x^2+2x-3\) to find the solution set of the following equation.
\[ \frac{x^2-5x+4}{x^2+2x-3}=1\]
\( \emptyset\)
\( \{1\}\)
\( \{-3;4\}\)
\( \{-3;1;4\}\)
2000005302
Level:
C
Use the graphs of the functions \(f(x)=x^2-x-6\) and \(g(x)=x-3\) to find the solution set of the following equation.
\[\frac{x^2-x-6}{x-3}=1\]
\( \{ -1\} \)
\( \{ 3\} \)
\( \{ -1;3\} \)
\( \{ -2;3\} \)