9000104303 Level: BAssuming \(a < 3\), solve the following inequality. \[ ax - 3\geq 3x - a \]\(\left (-\infty ,-1\right ] \)\(\left (-\infty ,-1\right )\)\(\left (-1,\infty \right )\)\(\mathbb{R}\)
9000104505 Level: ASolve the following equation with unknown \(x\) and a real parameter \(a\in\mathbb{R}\setminus\{-3,3\}\). \[\frac{a-x} {a-3} - \frac{6a} {a^{2}-9} = \frac{x-3} {a+3} \]\(\begin{array}{cc} \hline \text{Parameter} & \text{Solution set}\\ \hline a=0 & \emptyset \\ a\notin\{-3,0,3\} & \left\lbrace\frac{a^2-9}{2a}\right\rbrace \\\hline \end{array}\)\(\begin{array}{cc} \hline \text{Parameter} & \text{Solution set}\\ \hline a=0 & \mathbb{R} \\ a\notin\{-3,0,3\} & \left\lbrace\frac{a^2-9}{2a}\right\rbrace \\\hline \end{array}\)\(\begin{array}{cc} \hline \text{Parameter} & \text{Solution set}\\ \hline a=0 & \mathbb{R}\setminus\{0\} \\ a\notin\{-3,0,3\} & \left\lbrace\frac{a^2-9}{2a}\right\rbrace \\\hline \end{array}\)
9000104304 Level: BAssuming \(a < 0\), solve the following inequality. \[ \frac{x} {a}\geq 1 \]\(\left (-\infty ,a\right ] \)\(\left (-\infty ,a\right )\)\(\left [ a,\infty \right )\)\(\left (a,\infty \right )\)
9000104305 Level: BAssuming \(a > -1\), solve the following inequality. \[ \frac{2x} {a + 1} - 1 < 0 \]\(\left (-\infty , \frac{a+1} {2} \right )\)\(\left (-\frac{a+1} {2} , \frac{a+1} {2} \right )\)\(\left \{\frac{a+1} {2} \right \}\)\(\left (\frac{a+1} {2} ,\infty \right )\)
9000104307 Level: BAssuming \(a\in \left (0,2\right )\), solve the following inequality. \[ a\left (a - 2\right )x > 1 \]\(\left (-\infty , \frac{1} {a\left (a-2\right )}\right )\)\(\left ( \frac{1} {a\left (a-2\right )},\infty \right )\)\(\emptyset \)\(\left \{ \frac{1} {a\left (a-2\right )}\right \}\)
9000104308 Level: AAssuming \(a = \frac{1} {2}\), solve the following inequality. \[ 2a^{2}x - 1 > ax \]\(\emptyset \)\(\mathbb{R}\)\(\left ( \frac{1} {a\left (2a-1\right )},\infty \right )\)\(\left (-\infty , \frac{1} {a\left (2a-1\right )}\right )\)
9000104309 Level: AAssuming \(a = -1\), solve the following inequality. \[ a^{2}x - 1 < a - ax \]\(\emptyset \)\(\mathbb{R}\)\(\mathbb{R}\setminus \{- 1\}\)\(\mathbb{R}\setminus \{ - 1,0\}\)
9000104310 Level: BAssuming \(a\in \left (0,1\right )\), solve the following inequality. \[ 2a\left (1 - a\right )x > 3 \]\(\left ( \frac{3} {2a\left (1-a\right )},\infty \right )\)\(\left (- \frac{3} {2a\left (1-a\right )},\infty \right )\)\(\left (- \frac{3} {2a\left (1-a\right )}, \frac{3} {2a\left (1-a\right )}\right )\)\(\left (-\infty , \frac{3} {2a\left (1-a\right )}\right )\)
9000104401 Level: AFind a set of the values of the real parameter \(a\) which ensure that the following equation has no solution. \[ a^{2}x + 2ax - 3a = 0 \]\(\{ - 2\}\)\(\{2\}\)\(\{0\}\)\(\{ - 3,1\}\)
9000104402 Level: AFind a set of the values of the real parameter \(a\) which ensure that the following equation has no solution. \[ 2a^{2}x - ax - 2a = -1 \]\(\left \{0\right \}\)\(\left \{\frac{1} {2}\right \}\)\(\left \{-\frac{1} {2}\right \}\)\(\left \{-\frac{1} {2}, \frac{1} {2}\right \}\)