1003020201
Level:
A
Find the solution set of the following equation.
\[ 2-\frac{2-x}3=\frac x2+\frac{8-x}6 \]
\( \mathbb{R} \)
\( \emptyset \)
\( \{0\} \)
\( \{4\} \)
Linear equations and inequalities
1003020202
Level:
A
Assuming \( x\in\mathbb{N} \), find the solution set of the equation.
\[ 3x-\left[1+2\cdot(3x-2)\right]=9\]
\( \emptyset \)
\( \mathbb{N} \)
\( \{-2\} \)
\( \left\{\frac{14}9\right\} \)
1003020203
Level:
A
Find the solution set of the following equation.
\[ \frac{x+5}2-\frac{x+1}4=\frac{22+2x}8\]
\( \emptyset \)
\( \mathbb{R} \)
\( \{4\} \)
\( \{-4\} \)
1003020204
Level:
A
Assuming \( x\in\mathbb{Z} \), find the solution set of the equation.
\[ 3-6x+3\cdot\left\{x-\left[2-(x+1)\right]\right\}=0\]
\( \mathbb{Z} \)
\( \emptyset \)
\( \{1\} \)
\( \{0\} \)
1003037301
Level:
A
Five times the unknown number is greater by nine than one-half of the number. Find the number.
\( 2 \)
\( -2 \)
\( 1 \)
\( 10 \)
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.
\( 7 \)
\( 13 \)
\( 21 \)
\( 1 \)
1003037303
Level:
A
Two more than eight times of the unknown number is the same as one-third of the difference of one and the number. Find the number.
\( -\frac15 \)
\( -\frac7{23} \)
\( -\frac5{27} \)
\( -\frac7{21} \)
1003037304
Level:
A
The product of two consecutive natural numbers is the same as the sum of the square of the smaller one and eight. Find the smaller number.
\( 8 \)
\( 4 \)
\( 2 \)
There is not such a natural number.
1003037305
Level:
A
Suppose we increase the numerator of five-ninth by an integer and we decrease the denominator of five-ninth by the same integer. We get the fraction with numerator six times greater than the denominator. Find the integer.
\( 7 \)
\( 3 \)
There is no such an integer.
\( 1 \)
1003037306
Level:
A
The ratio of two more than five times \( x \) and five is equal to the sum of \( x \) and \( a \). Determine \( a \).
\( 0.4 \)
It is not possible to determine the number \( a \) uniquely without knowing the number \( x \).
\( 2 \)
\( 10 \)