Linear equations and inequalities
2110016205
Level:
B
Identify a picture that shows the correct solution set of the following inequality. The solution set is marked in red.
\[ -0.5x+\frac{2x+1}2\leq 2 \]
2110016204
Level:
B
Identify a picture that shows the correct solution set of the following inequality. The solution set is marked in red.
\[
0.5x + 2 < -2x +8
\]
2110016202
Level:
B
Solve the following inequality and choose the diagram that shows the correct solution set marked in red on the number line.
\[ 4.5 - 0.7x < 1 - 2.1x\]
2010016203
Level:
B
Find the minimal integer which satisfies the following inequality.
\[
3x - 1 \leq 7x-8
\]
\( 2 \)
\( 0 \)
\(3\)
\( 1 \)
2010016201
Level:
B
Find the linear inequality of which the solution set is shown in red in the graph below.
\( \frac{x+4}2 > 6-x \)
\( \frac{x-4}2 > 6-x \)
\( x+2 \geq 6-x \)
\( \frac{x+4}2 < 6-x \)
2010015407
Level:
A
Find the solution set of the following equation.
\[x\sqrt5 -2\sqrt{10}x=-35\]
\( \left\{ \sqrt5+2\sqrt{10}\right\}\)
\( \left\{ \sqrt5-2\sqrt{10}\right\}\)
\( \left\{ -\sqrt5+\sqrt{10}\right\}\)
\( \left\{ \sqrt5-\sqrt{10}\right\}\)
2010015406
Level:
A
Find the solution set of the following equation.
\[2\sqrt2 x-5 =x\sqrt3\]
\( \left\{ 2\sqrt2+\sqrt3\right\}\)
\( \left\{ 2\sqrt2-\sqrt3\right\}\)
\( \left\{ \sqrt2+\sqrt3\right\}\)
\( \left\{ \sqrt2-\sqrt3\right\}\)
2010015405
Level:
C
The ratio of ages of a mother and her daughter is \(3: 1\). Ten years ago, the ratio of their ages was \(8 : 1\). How old is the mother today?
\(42\) years
\(32\) years
\(52\) years
\(45\) years
2010015404
Level:
C
The average age in the group of six persons is \(48\) years. The average age of the first five of them is \(51\) years. How old is the sixth person?
\(33\) years
\(32.5\) years
\(39.5\) years
\(43\) years