1003037301
Level:
A
Five times the unknown number is greater by nine than one-half of the number. Find the number.
\( 2 \)
\( -2 \)
\( 1 \)
\( 10 \)
Linear Equations and Inequalities
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.
\[ 2-\frac{2-x}3=\frac x2+\frac{8-x}6 \]
\( \mathbb{R} \)
\( \emptyset \)
\( \{0\} \)
\( \{4\} \)
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 \(x\neq 0\)
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 \((3x - 1)\)