2010015903
Level:
B
Find the solution set of the following inequality.
\[
\frac{x -2}
{x +3} > 1
\]
\(( -\infty; -3) \)
\((-3;\infty) \)
\(( -\infty; 2) \)
\((2;\infty) \)
Rational equations and inequalities
2010015904
Level:
B
An inequality is solved graphically as shown in the picture. The solution is marked in red. Choose the corresponding inequality.
\(3\leq \frac{x-2}
{x} \)
\(3\geq -\frac{2}
{x} \)
\(3\geq \frac{x-2}
{x} \)
\(3\leq -\frac{2}
{x} \)
2010015905
Level:
B
Find the solution set of the following inequality.
\[
\frac{-1}
{x^2+x-20} \geq 0
\]
\( (-5;4)\)
\(\emptyset\)
\((-\infty;-5) \cup (4;\infty) \)
\((-4;5) \)
2010015906
Level:
B
Find the solution set of the inequality.
\[ \left(x^2+4\right)\left(x^2+2\right)\leq0 \]
\( \emptyset\)
\( \left(-2;-\sqrt2\right)\)
\(\mathbb{R}\)
\( \left(-2;-\sqrt2\right) \cup \left(\sqrt2;2\right)\)
2110015907
Level:
B
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.
\[
\frac{-x}
{x + 1} > 0
\]
9000018005
Level:
B
Find all real values of \(x\) for which the fraction \(\frac{3}{2-x}\) is positive.
\(x < 2\)
\(x < -2\)
\(x > -2\)
\(x > 2\)
9000018105
Level:
B
Find all the values of \(x\)
which ensure that the following fraction is positive.
\[
- \frac{3}
{5 - 2x}
\]
\(x > \frac{5}
{2}\)
\(x < \frac{5}
{2}\)
\(x < -\frac{5}
{2}\)
\(x > -\frac{5}
{2}\)
9000021804
Level:
B
Solve the following inequality.
\[
\frac{1}
{x - 3}\leq \frac{1}
{2 - x}
\]
\(x\in (-\infty ;2)\cup \left [ \frac{5}
{2};3\right )\)
\(x\in (-\infty ;2)\cup \left [ \frac{5}
{3};2\right ] \)
\(x\in \left (-\infty ; \frac{5}
{2}\right ] \cup \left (3;\infty \right )\)
\(x\in \left [ \frac{5}
{2};\infty \right )\)
9000021806
Level:
B
Solve the following inequality.
\[
\frac{1 - 3x}
{x + 2} \geq 0
\]
\(x\in \left (-2; \frac{1}
{3}\right ] \)
\(x\in \left [ \frac{1}
{3};\infty \right )\)
\(x\in \left (\frac{1}
{3};\infty \right )\)
\(x\in (-\infty ;-2)\cup \left [ \frac{1}
{3};\infty \right )\)
9000021809
Level:
B
Solve the following inequality.
\[
\frac{2x + 4}
{x - 1} < 1
\]
\(x\in (-5;1)\)
\(x\in (-\infty ;5)\)
\(x\in (1;\infty )\)
\(x\in (-\infty ;-3)\cup (1;\infty )\)