2010015406
Level:
A
Find the solution set of the following equation.
\[2\sqrt2 x-5 =x\sqrt3\]
\( \left\{ 2\sqrt2+\sqrt3\right\}\)
\( \left\{ 2\sqrt2-\sqrt3\right\}\)
\( \left\{ \sqrt2+\sqrt3\right\}\)
\( \left\{ \sqrt2-\sqrt3\right\}\)
Linear equations and inequalities
2010015407
Level:
A
Find the solution set of the following equation.
\[x\sqrt5 -2\sqrt{10}x=-35\]
\( \left\{ \sqrt5+2\sqrt{10}\right\}\)
\( \left\{ \sqrt5-2\sqrt{10}\right\}\)
\( \left\{ -\sqrt5+\sqrt{10}\right\}\)
\( \left\{ \sqrt5-\sqrt{10}\right\}\)
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 \(\frac{1}
{18}\)
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 \((4x + 2)\)
1003031102
Level:
B
The intended capacity of an IT course was filled by \( 20 \) people interested to attend.
How many participants can check out without decreasing the course occupancy under \( 72\% \)?
at most \( 5 \)
at most \( 6 \)
at most \( 15 \)
at most \( 14 \)