2010015403
Level:
A
Choose the equation whose graphical solution is in the picture.
\( -\frac49x+1=\frac29x-2\)
\( -\frac94x+1=\frac29x-2\)
\( -\frac49x+1=\frac92x-2\)
\( -\frac94x+1=\frac92x-2\)
Linear equations and inequalities
2010015402
Level:
A
Choose the equation whose graphical solution is in the picture.
\( \frac25x-2=-4x+4\)
\( \frac52x-2=-4x+4\)
\( \frac12x-2=-x+4\)
\( \frac25x-2=-x+4\)
2010015401
Level:
A
Choose the equation whose graphical solution is in the picture.
\( \frac12x+2=5-x\)
\( x+2=-x+5 \)
\( \frac14x+2=5-x \)
\( -x+2=5-\frac12x \)
2010011506
Level:
B
Assuming \(x\in \mathbb{R}\),
find the solution set of the following inequality.
\[
(x-2)^2+(2+x)^2 \leq 8+2x^2
\]
\(\mathbb{R}\)
\(\emptyset \)
\([ 0;8]\)
\([ -8;0]\)
2010011505
Level:
B
Assuming \(x\in \mathbb{R}\),
find the solution set of the following inequality.
\[
(x+3)^2-1+3x^2 >(2-2x)^2
\]
\(\left( -\frac27;\infty\right)\)
\(\left( \frac27;\infty\right)\)
\(\left( -\infty;\frac27 \right)\)
\(\left( -\infty;-\frac27\right)\)
2010011504
Level:
B
We are given the inequality \( 2x+\frac{3-4x}2 < \frac72 \). Decide which of the following inequalities is equivalent to the given inequality, i.e. which of the following inequalities was obtained from the given inequality by equivalent transformations.
\( 0\cdot x < 4 \)
\( 0\cdot x < -4\)
\( 0\cdot x > 4 \)
\( 2\cdot x > -4 \)
2010011503
Level:
B
Assuming \(x\in \mathbb{R}\),
find the solution set of the following system.
\[
3 x -1 \leq 2x + 7 \leq 7x-8
\]
\(x\in [ 3;8] \)
\(x\in (-\infty ;3] \)
\(x\in [ 8;\infty )\)
\( x \in \mathbb{R}\setminus (3;8)\)
2010011502
Level:
B
Solve the following inequality:
\[
26 -2\left (9x +4 \right ) > 6\left (3-3x\right )
\]
\( x \in \emptyset\)
\(x\in (-\infty ;0) \)
\(x\in \left (-\infty;\infty \right )\)
\(x\in (0;\infty )\)
2010011501
Level:
B
Solve the following inequality:
\[
6 -3\left (2x +4 \right ) \leq 2\left (3-3x\right )
\]
\(x\in \left (-\infty;\infty \right )\)
\(x\in (-\infty ;-1]\)
\(x\in [ -1;\infty )\)
\( x \in \emptyset\)
2010011202
Level:
C
Students registered for sports camps. For the biking camp registered by \( 12 \) students more than for the boating camp. After some time one of the students switched his registration from the boating camp to the biking camp. Now, there is three times more bikers than boaters. How many students registered originally for the biking camp?
\( 20 \)
\( 21 \)
\( 7 \)
\( 8 \)