1003020202
Level:
A
Assuming \( x\in\mathbb{N} \), find the solution set of the equation.
\[ 3x-\left[1+2\cdot(3x-2)\right]=9\]
\( \emptyset \)
\( \mathbb{N} \)
\( \{-2\} \)
\( \left\{\frac{14}9\right\} \)
Linear equations and inequalities
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.
\[
x + 2 > 2x + 3 > 3x + 5
\]
\((-\infty ;-2)\)
\((-2;+\infty )\)
\((-\infty ;-1)\)
\((-2;-1)\)
9000024107
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.
\[
8x = \frac{x + 1}
{4} + 1
\]
multiply by \(4\)
multiply by \(\frac{1}
{8}\)
multiply by \(\frac{1}
{4}\)
multiply by \((x + 1)\),
assuming \(x\neq - 1\)
subtract \((x + 1)\)
subtract \(1\)
9000024108
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.
\[
\frac{x + 1}
{2} -\frac{x - 2}
{3} = \frac{x}
{4}
\]
multiply by \(12\)
multiply by \(2\)
multiply by \(3\)
multiply by \(4\)
multiply by \(24\)
multiply by \((2x + 1)(x - 2)x\),
assuming \(x\not \in \left \{-\frac{1}
{2};2;0\right \}\)
9000024110
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.
\[
11x - 2 = 2 - 4x
\]
add \((4x + 2)\)
multiply by \(\frac{1}
{11}\)
multiply by \(\left (-\frac{1}
{4}\right )\)
add \((-11x + 4x)\)
subtract \((4x + 2)\)
add \((4x + 2)\)
9000024101
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.
\[
3x + 2 = -5x + 1
\]
add \((5x - 2)\)
multiply by \(\frac{1}
{3}\)
multiply by \(-\frac{1}
{5}\)
add \((-3x + 2)\)
add \((5x + 1)\)
add \((3x - 1)\)
9000024102
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.
\[
x + \frac{x}
{6} = \frac{x}
{15} + 1
\]
multiply by \(30\)
multiply by \(6\)
multiply by \(15\)
subtract \((1 + x)\)
subtract \(\left (\frac{x}
{6} + \frac{x}
{15}\right )\)
subtract \(\left (\frac{x}
{6} + 1\right )\)
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 \(\frac{1}
{18}\)