9000083701
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{x^{2} - 16}
{2x - 8}
\]
\(x = -4\)
\(x = 4\)
\(x =\pm 4\)
\(x = 0\)
A
9000081403
Level:
A
Find the inequality which describes the set graphed in the picture.
\(|x + 1| > 2,\ x\in \mathbb{R}\)
\(|x - 1| < 2,\ x\in \mathbb{R}\)
\(|x + 1| < 2,\ x\in \mathbb{R}\)
\(|x - 1| > 2,\ x\in \mathbb{R}\)
\(|x - 2| > 1,\ x\in \mathbb{R}\)
9000083702
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{x^{2} + 6x + 9}
{x^{2} - 9}
\]
The expression never equals zero.
\(x =\pm 3\)
\(x = 3\)
\(x = -3\)
9000081404
Level:
A
Find the inequality which describes the set graphed in the picture.
\(|2 + x| > 1,\ x\in \mathbb{R}\)
\(|2 + x| < 1,\ x\in \mathbb{R}\)
\(|2 - x| > 1,\ x\in \mathbb{R}\)
\(|2 - x| < 1,\ x\in \mathbb{R}\)
\(|1 + x| > 2,\ x\in \mathbb{R}\)
9000083703
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{x^{3} - x}
{x - 1}
\]
\(x = -1,\ x = 0\)
\(x = 0\)
\(x = 1\)
\(x = -1,\ x = 0,\ x = 1\)
9000081405
Level:
A
Find the inequality which describes the set graphed in the picture.
\(|2 - x| < 1,\ x\in \mathbb{R}\)
\(|2 + x| > 1,\ x\in \mathbb{R}\)
\(|2 + x| < 1,\ x\in \mathbb{R}\)
\(|2 - x| > 1,\ x\in \mathbb{R}\)
\(|1 - x| < 2,\ x\in \mathbb{R}\)
9000083704
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{x^{2} - 4x + 4}
{x(x - 2)}
\]
The expression never equals zero.
\(x = 0\)
\(x = 2\)
\(x = -2,\ x = 0\)
9000083705
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{2x(x + 2)(x - 3)}
{x^{2} - 4}
\]
\(x = 0,\ x = 3\)
\(x = -2,\ x = 0,\ x = 3\)
\(x = 0\)
\(x =\pm 2\)
9000083706
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{4x^{2} - 36}
{4x^{2} + 24x + 36}
\]
\(x = 3\)
\(x = 4\)
\(x = -3,\ x = 3\)
The expression never equals zero.
9000083707
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{4x^{3} + 20x^{2} + 25x}
{x + 1}
\]
\(x = 0,\ x = -\frac{5}
{2}\)
\(x = 0\)
\(x = -\frac{5}
{2}\)
\(x = -1\)