A

9000023804

Level: 
A
Identify a true statement which concerns to the following equation. \[ \sqrt{x + 3} = x - 3 \]
The solution is in the interval \((5,8)\).
The solution is in the interval \([ - 2,2] \).
The solution is in the interval \([ - 3,1)\).
The solution is in the interval \([ 3,5)\).

9000023809

Level: 
A
Identify a true statement which concerns to the following equation. \[ \sqrt{16 - 5x} = 2 - x \]
The solution \(x\) satisfies \(|x| > 3\).
The solution \(x\) satisfies \(|x| < 3\).
The solution \(x\) satisfies \(|x + 1| < 3\).
The solution \(x\) satisfies \(|x + 1| > 3\).

9000023709

Level: 
A
Identify a true statement which concerns the following pair of equations. \[ \begin{aligned} \sqrt{ 5 - x} & = 2 &\text{(1)} \\ \sqrt{x + 5} & = 4 &\text{(2)} \end{aligned} \]
The solution of (1) is smaller than the solution of (2).
The solutions of both equations are prime numbers.
The solution of (1) is bigger than the solution of (2).
The solution of (1) equals to the solution of (2).

9000022802

Level: 
A
Find all \(x\in \mathbb{R}\) for which the following expression is undefined. \[ \log \left (2x^{2} + 4x - 6\right ) \]
\(\left [ -3,1\right ] \)
\(\left (-\infty ,-3\right )\cup \left (1,\infty \right )\)
\(\left (-3,1\right )\)
\(\left (-\infty ,-3\right ] \cup \left [ 1,\infty \right )\)

9000023805

Level: 
A
Identify a true statement about the following equation. \[ \sqrt{6 + x} = -x \]
The solution is in the set \(\left \{x\in \mathbb{R} : -4 < x\leq - 1\right \}\).
The solution is in the set \(\left \{x\in \mathbb{R} : 1\leq x\leq 5\right \}\).
The solution is in the set \(\left \{x\in \mathbb{R} : -6\leq x\leq - 3\right \}\).
The solution is in the set \(\left \{x\in \mathbb{R} : -2 < x < 3\right \}\).

9000020408

Level: 
A
Which of the given equations have at least one root the same? \[ \begin{aligned} x^{2} + 8x + 15 & = 0 &\text{(1)} \\x^{2} - 8x + 15 & = 0 &\text{(2)} \\x^{2} +\phantom{ 8}x - 12 & = 0 &\text{(3)} \\x^{2} - 2x -\phantom{ 1}8 & = 0 &\text{(4)} \\\end{aligned}\]
equations (2) and (3)
equations (1) and (3)
equations (2) and (4)
Such a pair does not exist.

9000020006

Level: 
A
Identify a true statement referring to the solution of the following equation. \[ \sqrt{3x - 8} = x - 6 \]
The equation has a unique solution and this solution is an odd number.
The equation has two solutions, the sum of these solutions is divisible by \(5\).
The equation has a unique solution and this solution is an even number.
The equation does not have a solution in \(\mathbb{R}\).