B

9000020902

Level: 
B
The solution of the given set of equations can be interpreted as the intersection of the curves shown in the figure. Find the solution of the system in \(\mathbb{R}\times \mathbb{R}\). \[ \begin{alignedat}{80} &4x^{2} & + &y &^{2} & = &20 & & & & & & & & & \\ &2x & + &y & & = &6 & & & & & & & & & \\\end{alignedat}\]
\([1;4],\ [2;2]\)
\([2;2]\)
\([1;4]\)
no solution

9000021803

Level: 
B
Solve the following inequality. \[ (3x - 1)(2 - 4x) < 0 \]
\(x\in \left (-\infty ; \frac{1} {3}\right )\cup \left (\frac{1} {2};\infty \right )\)
\(x\in \left (\frac{1} {3}; \frac{1} {2}\right )\)
\(x\in \left (-\infty ; \frac{1} {2}\right )\)
\(x\in \left (\frac{1} {3};\infty \right )\)

9000021804

Level: 
B
Solve the following inequality. \[ \frac{1} {x - 3}\leq \frac{1} {2 - x} \]
\(x\in (-\infty ;2)\cup \left [ \frac{5} {2};3\right )\)
\(x\in (-\infty ;2)\cup \left [ \frac{5} {3};2\right ] \)
\(x\in \left (-\infty ; \frac{5} {2}\right ] \cup \left (3;\infty \right )\)
\(x\in \left [ \frac{5} {2};\infty \right )\)

9000021810

Level: 
B
Find all the values of \(x\) for which the following expression takes on values smaller than or equal to \(1\). \[ \frac{x + 1} {x - 1} - \frac{1} {x + 1} \]
\(x\in (-\infty ;-3] \cup (-1;1)\)
\(x\in (-\infty ;-3] \)
\(x\in (-\infty ;-1)\cup (-1;1)\cup (1;\infty )\)
\(x\in [ - 3;-1)\)