Radical Equations and Inequalities

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 \(|x + 1| > 3\).

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

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).

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