Radical Equations and Inequalities

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 \(\left \{x\in \mathbb{R} : -2 < x < 3\right \}\).

9000022305

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

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 \(x_{2}\).
\(|x_{1}| = |x_{2}|\)
\(|x_{1}| < |x_{2}|\)
\(|x_{1}| > |x_{2}|\)
\(5|x_{1}| = |x_{2}|\)

9000023703

Level: 
A
Identify a true statement which concerns the following equation. \[ \sqrt{x + 1} = 2 \]
The solution is a number from the interval \([ 2,5)\).
The solution is a number from the interval \([ - 1,2] \).
The solution is a number from the interval \([ - 2,3)\).
The solution is a number from the interval \((4,7)\).

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 \(4\).