1103049402
Level:
A
Choose the picture which represents the graphical solution of the following equation.
\[ \frac23 x+\frac13=1-\frac32 x \]
Linear equations and inequalities
1103049401
Level:
A
Choose the equation whose graphical solution is in the picture.
\( \frac12x-3=-\frac52x-5 \)
\( \frac12x-3=-2x-5 \)
\( 2x-3=-\frac52 x-5 \)
\( 2x-3=-2x-5 \)
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 \( 500\,\mathrm{CZK} \).