A

9000024109

Level: 
A
Identify the optimal first step to solve the following equation. The operation is intended to be used on both sides of the equation. \[ \frac{2x + 1} {x - 1} + \frac{x + 1} {x - 1} = \frac{11} {2} \]
multiply by \(2(x - 1)\), assuming \(x\neq 1\)
multiply by \((2x + 1)\), assuming \(x\neq -\frac{1} {2}\)
multiply by \((x + 1)\), assuming \(x\neq - 1\)
multiply by \(\frac{1} {2x+1}\), assuming \(x\neq -\frac{1} {2}\)
multiply by \(\frac{1} {x+1}\), assuming \(x\neq - 1\)
multiply by \(2(2x + 1)(x + 1)\), assuming \(x\neq -\frac{1} {2}\) and \(x\neq - 1\)

9000024406

Level: 
A
Identify the values of real parameters \(a\) and \(b\) such that the graph of the function \[ f(x)= |x + a| + b \] corresponds to the picture.
\(\ \ a = 3,\quad \phantom{ -} b = 2\)
\(\ \ a = 2,\quad \phantom{ -} b = 3\)
\(\ \ a = 2,\quad \phantom{ -} b = -3\)
\(\ \ a = -3,\quad b = 2\)

9000024108

Level: 
A
Identify the optimal first step to solve the following equation. The operation is intended to be used on both sides of the equation. \[ \frac{x + 1} {2} -\frac{x - 2} {3} = \frac{x} {4} \]
multiply by \(12\)
multiply by \(2\)
multiply by \(3\)
multiply by \(4\)
multiply by \(24\)
multiply by \((2x + 1)(x - 2)x\), assuming \(x\not \in \left \{-\frac{1} {2},2,0\right \}\)

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