9000023806
Level:
A
Identify a true statement which concerns to the following equation.
\[
\sqrt{3x + 4} = x
\]
The solution divides \(4\).
The solution divides \(1\).
The solution divides \(2\).
The solution divides \(3\).
Radical Equations and Inequalities
9000023807
Level:
A
Identify a true statement which concerns to the following equation.
\[
\sqrt{x + 3} = \frac{x}
{2}
\]
The solution is a multiple of \(2\).
The solution is a multiple of \(4\).
The solution is a multiple of \(8\).
The solution is a multiple of \(12\).
9000023808
Level:
A
Identify a true statement which concerns to the following equation.
\[
\sqrt{x + 5} = x + 3
\]
The solution \(x\)
satisfies \(|x| = 1\).
The solution \(x\)
satisfies \(|x| = 2\).
The solution \(x\)
satisfies \(|x| = 3\).
The solution \(x\)
satisfies \(|x| = 4\).
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).
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 \(\left \{x\in \mathbb{R} : -2 < x < 3\right \}\).
9000020009
Level:
A
Choose the equation which is obtained by squaring both
sides of the following equation.
\[
\sqrt{3x + 2} = x - 6
\]
\(x^{2} - 15x + 34 = 0\)
\(x^{2} - 3x - 38 = 0\)
\(x^{2} - 3x - 34 = 0\)
\(x^{2} - 15x - 38 = 0\)
9000020010
Level:
A
Choose the equation which is obtained by squaring both
sides of the following equation.
\[
\sqrt{x^{2 } - x + 5} = 2x - 5
\]
\(3x^{2} - 19x + 20 = 0\)
\(x^{2} + 3x + 20 = 0\)
\(3x^{2} + x - 30 = 0\)
\(3x^{2} + x + 20 = 0\)
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
\(\mathbb{R}\).
9000020007
Level:
A
Identify a true statement referring to the solution of the following equation.
\[
\sqrt{x^{2 } - 4} = x + 1
\]
The equation does not have a solution in
\(\mathbb{R}\).
The equation has a unique negative solution.
The equation has a unique positive solution.
The equation has two solutions.