A

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 \(\frac{1} {18}\)

9000023908

Level: 
A
Let \([x;y]\) be the solution of the system \[\begin{aligned} 2x - y & = -1, & & \\4x - y & = 1. & & \end{aligned}\] In the following list identify a true statement.
\(y\) is a prime number.
\(x\) is a prime number.
\(x + y\) is a prime number.
\(x - y\) is a prime number.

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 \(x\neq 0\)

9000024406

Level: 
A
Identify the values of real parameters \(a\) and \(b\) such that the graph of the function \[ f(x)= |x + a| + b \] corresponds to the picture.
\(\ \ a = 3,\quad \phantom{ -} b = 2\)
\(\ \ a = 2,\quad \phantom{ -} b = 3\)
\(\ \ a = 2,\quad \phantom{ -} b = -3\)
\(\ \ a = -3,\quad b = 2\)

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 \(1\)

9000025805

Level: 
A
In the following list identify a true statement on the function \(f\). \[ f(x) = (x + 1)(x + 2)(x - 3) \]
\(f(x) < 0 \iff x\in (-\infty ;-2)\cup (-1;3)\)
\(f(x) < 0 \iff x\in \left (-\infty ;-\frac{3} {2}\right )\cup (1;3)\)
\(f(x) < 0 \iff x\in \left (-\infty ;-\frac{3} {2}\right )\cup (3;\infty )\)
\(f(x) < 0 \iff x\in \left (-\frac{3} {2};-1\right )\cup (3;\infty )\)

9000023810

Level: 
A
Denote by \(x_{1}\) the solution of the equation \[ \sqrt{6 - 2x} = -x - 1 \] and by \(x_{2}\) the solution of the equation \[ \sqrt{2x + 6} = 9 - x. \] Identify a correct statement about \(x_{1}\) and \(x_{2}\).
\(|x_{1}| = |x_{2}|\)
\(|x_{1}| < |x_{2}|\)
\(|x_{1}| > |x_{2}|\)
\(5|x_{1}| = |x_{2}|\)