2010009006
Level:
A
Find the solution set of the following equation.
\[(x-2)^2+(2+x)^2=8+2x^2 \]
\( \mathbb{R}\)
\( \{-1\} \)
\( \{2\} \)
\( \{-2\} \)
Linear equations and inequalities
2010009005
Level:
A
Find the solution set of the following equation.
\[(x+3)^2-(2-2x)^2=1-3x^2 \]
\( \left\{-\frac27\right\} \)
\( \{2\} \)
\( \left\{\frac72\right\} \)
\( \emptyset \)
2010009004
Level:
A
Find the solution set of the following equation.
\[x-3[x-5(x-4)]=10(x-3) \]
\( \{10\} \)
\( \left\{-\frac{10}9\right\} \)
\( \{-14\} \)
\( \emptyset \)
2010009003
Level:
A
Find the solution set of the following equation.
\[3x-2[x-3(x+1)]=7x+6 \]
\( \mathbb{R} \)
\( \{-1\} \)
\( \{0\} \)
\( \emptyset \)
2010009002
Level:
A
Find the solution set of the following equation.
\[\frac{3+2x}2-\frac76=5x-\frac{12x-1}3 \]
\( \mathbb{R} \)
\( \{1\} \)
\( \{0\} \)
\( \emptyset \)
2010009001
Level:
A
Find the solution set of the following equation.
\[\frac{x+5}3-\frac x2=\frac{2x-2}3-\frac{x-3}2 \]
\( \left\{\frac52 \right\} \)
\( \left\{\frac{23}2\right\} \)
\( \mathbb{R} \)
\( \emptyset \)
2000002905
Level:
B
Determine all the natural numbers that are solutions of the inequality:
\[
-\frac{9}{8} \leq -\frac{x}{4}
\]
\( x \in \{ 1;2;3;4\} \)
\( x \in \mathbb{N} \)
\( x \in \{0; 1;2;3;4\} \)
\( x \in \{ 1;2;3;4;5\} \)
2000002904
Level:
B
Determine the largest integer that is the solution of the inequality:
\[
-1.2x > -1.44
\]
\( 1\)
\( 2 \)
\( 0 \)
\( -1\)
2000002903
Level:
B
Determine the largest integer that is the solution of the inequality:
\[
-0.16x > 6.4
\]
\( -41\)
\( -39 \)
\( -40\)
\( -42\)
2000002902
Level:
B
Determine the smallest integer that is the solution of the inequality:
\[
-5.2x < 1.3\]
\( 0\)
\( -1\)
\( 4\)
\( 1\)