1003037302
Level:
A
The sum of three consecutive odd numbers is twenty greater than the smallest of these numbers. Find the smallest one of the three unknown odd numbers.
\( 7 \)
\( 13 \)
\( 21 \)
\( 1 \)
Linear equations and inequalities
1003037301
Level:
A
Five times the unknown number is greater by nine than one-half of the number. Find the number.
\( 2 \)
\( -2 \)
\( 1 \)
\( 10 \)
1003020204
Level:
A
Assuming \( x\in\mathbb{Z} \), find the solution set of the equation.
\[ 3-6x+3\cdot\left\{x-\left[2-(x+1)\right]\right\}=0\]
\( \mathbb{Z} \)
\( \emptyset \)
\( \{1\} \)
\( \{0\} \)
1003020203
Level:
A
Find the solution set of the following equation.
\[ \frac{x+5}2-\frac{x+1}4=\frac{22+2x}8\]
\( \emptyset \)
\( \mathbb{R} \)
\( \{4\} \)
\( \{-4\} \)
1003020202
Level:
A
Assuming \( x\in\mathbb{N} \), find the solution set of the equation.
\[ 3x-\left[1+2\cdot(3x-2)\right]=9\]
\( \emptyset \)
\( \mathbb{N} \)
\( \{-2\} \)
\( \left\{\frac{14}9\right\} \)
1003020201
Level:
A
Find the solution set of the following equation.
\[ 2-\frac{2-x}3=\frac x2+\frac{8-x}6 \]
\( \mathbb{R} \)
\( \emptyset \)
\( \{0\} \)
\( \{4\} \)
9000039002
Level:
B
Assuming \(x\in \mathbb{Z}\),
find the solution set of the following system.
\[
-3\leq 2(x + 2)\leq 6
\]
\(\{ - 3;-2;-1;0;1\}\)
\(\{ - 4;-2;-1;0;1\}\)
\(\{ - 3;-2;-1;0\}\)
\(\{0;1\}\)
9000039003
Level:
B
Assuming \(x\in \mathbb{R}\),
find the solution set of the following system.
\[
x + 2 > 2x + 3 > 3x + 5
\]
\((-\infty ;-2)\)
\((-2;+\infty )\)
\((-\infty ;-1)\)
\((-2;-1)\)
9000024103
Level:
A
Identify the optimal first step to solve the following equation. The operation is
intended to be used on both sides of the equation.
\[
\frac{x + 5}
{9} -\frac{x}
{6} = \frac{x - 2}
{9} + \frac{x - 3}
{9}
\]
multiply by \(18\)
multiply by \(6\)
multiply by \(9\)
multiply by \(54\)
multiply by \(\frac{1}
{9}\)
multiply by \(\frac{1}
{18}\)
9000024104
Level:
A
Identify the optimal first step to solve the following equation. The operation is
intended to be used on both sides of the equation.
\[
5x = \frac{2 + x}
{5}
\]
multiply by \(5\)
multiply by \(\frac{1}
{5}\)
multiply by \(\frac{1}
{2}\)
multiply by \(2\)
multiply by \(\frac{1}
{x}\),
assuming \(x\neq 0\)
multiply by \(x\),
assuming \(x\neq 0\)