Radical equations and inequalities

9000023704

Level: 
A
Identify a true statement which concerns the following equation. \[ \sqrt{x + 20} = 4 \]
The solution is from the set \(B = \left \{x\in \mathbb{R} : -6\leq x\leq - 2\right \}\).
The solution is from the set \(A = \left \{x\in \mathbb{R} : -4 < x\leq - 1\right \}\).
The solution is from the set \(C = \left \{x\in \mathbb{R} : -7\leq x\leq - 5\right \}\).
The solution is from the set \(D = \left \{x\in \mathbb{R} : -3 < x < 0\right \}\).

9000023707

Level: 
A
Identify a true statement which concerns the following equation. \[ \sqrt{3x - 5} = 4 \]
The solution is a prime number.
The solution is from the interval \([ - 5;5] \).
The solution is from the set \(A = \left \{x\in \mathbb{R} : -4 < x\leq 3\right \}\).
The solution is a multiple of \(4\).

9000023708

Level: 
A
Identify a true statement which concerns the following equation. \[ \sqrt{x + 5} = x - 1 \]
The solution is an even number.
The solution is from the interval \([ - 2;2)\).
The solution is from the set \(A = \left \{x\in \mathbb{R} : -1\leq x < 3\right \}\).
The solution is a divisor of \(6\).

9000023710

Level: 
A
Identify a true statement which concerns the following pair of equations. \[ \begin{aligned} \sqrt{ 2x + 17} & = 3 &\text{(1)} \\ \sqrt{8 - 4x} & = 4 &\text{(2)} \end{aligned} \]
The product of the solutions of (1) and (2) is \(8\).
The sum of the solutions of (1) and (2) is \(- 2\).
The quotient of the solution of (1) divided by the solution of (2) is \(- 2\).
The quotient of the solution of (2) divided by the solution of (1) is \(- 0.5\).

9000023803

Level: 
A
In the following list identify a true statement referring to the solution of the following equation. \[ \sqrt{x + 3} = 3 + x \]
The difference of the bigger and smaller solutions is \(1\).
The difference of the bigger and smaller solutions is \(- 1\).
The difference of the smaller and the bigger solutions is \(1\).
The difference of the smaller and twice the bigger solutions is \(- 1\).

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 \([ 3;5)\).

9000022305

Level: 
A
Find the domain of the following expression. \[ \sqrt{-x^{2 } + 16x - 63} \]
\(\left [ 7;9\right ] \)
\(\left (-\infty ;7\right )\cup \left (9;\infty \right )\)
\(\left (-\infty ;-7\right ] \cup \left [ 9;\infty \right )\)
\(\left (7;9\right )\)
\(\left [ -7;9\right ] \)