1103049401
Level:
A
Choose the equation whose graphical solution is in the picture.
\( \frac12x-3=-\frac52x-5 \)
\( \frac12x-3=-2x-5 \)
\( 2x-3=-\frac52 x-5 \)
\( 2x-3=-2x-5 \)
Linear Equations and Inequalities
1103049506
Level:
B
Which graph shows in red the solution set of the following inequality? (Note: If the graph does not show in red any interval, then it means that the inequality has no solution.)
\[ \frac x3-\frac{2x+1}6 < 4 \]
1103049505
Level:
B
Which graph shows in red the solution set of the following inequality?
\[ 2x \geq \frac{6-4x}2 \]
1103049504
Level:
B
Which inequality has the solution set graphed in red in the picture?
\( \frac{5-2x}2 < \frac 72 \)
\( \frac{5-2x}2 > \frac72 \)
\( \frac{5-2x}2 > 4 \)
\( \frac{5-2x}2 < 7 \)
1103049503
Level:
B
Identify a picture that shows the correct solution set of the following inequality. The solution set is marked in red.
\[ 2x-\frac{1+4x}4\geq-2 \]
1103049502
Level:
B
Find the linear inequality of which the solution set is shown in red in the graph below.
\( 2x+2 < \frac x4-\frac 12 \)
\( 2x+2 > \frac{x-2}4 \)
\( 2x+2 < -\frac x2+2 \)
\( \frac x2+2 < \frac x4-\frac12 \)
1103049501
Level:
B
Find the linear inequality of which the solution set is shown in red in the graph below.
\( x+2\geq\frac{2-x}2 \)
\( x+2\leq-\frac x2+1 \)
\( x+2>\frac{2-x}2 \)
\( x+2 < -\frac x2+1 \)
1003031104
Level:
C
Dan and Jane took a bike trip. Dan rode for \( 3 \) hours at constant speed. Jane rode for half an hour longer at the speed of \( 4\,\mathrm{kph} \) less than Dan’s speed. Identify, which of the following statements about Dan’s speed is true.
The speed is less than \( 28\,\mathrm{kph} \).
The speed is greater than \( 28\,\mathrm{kph} \).
The speed is less than \( 20\,\mathrm{kph} \).
The speed is greater than \( 24\,\mathrm{kph} \).
1003031103
Level:
C
Five litres of a quality wine in by yourself provided bottles cost more than three and a half litres of the same wine in a bigger wine container. The container price is \( 150\,\mathrm{CZK} \). Complete the next statement so that it is true. The price of one litre of this quality wine is
greater than \( 100\,\mathrm{CZK} \).
less than \( 100\,\mathrm{CZK} \).
greater than \( 350\,\mathrm{CZK} \).
greater than \( 500\,\mathrm{CZK} \).
1003031102
Level:
B
The intended capacity of an IT course was filled by \( 20 \) people interested to attend.
How many participants can check out without decreasing the course occupancy under \( 72\% \)?
at most \( 5 \)
at most \( 6 \)
at most \( 15 \)
at most \( 14 \)