Inequalities II - Challenging

Question 1: Solve the inequality:

\frac{4 x - 4}{x + 4} < x

A

x \in (- 4; 4)

B

x \in (- 6; - 5) \cup (- 4; + \infty)

C

x \in (- 4; + \infty)

D

x \in [- 4; + \infty)

Question 2: Solve the inequality:

\frac{1}{|x| + 1} > 1

A

x \in (- 1; 1)

B

x \in (- \infty; 1)

C

x = 0

D

х \in \emptyset

Question 3: Solve the inequality:

|\frac{1}{x + 3}| > 1

for

x < - 5

A

x = - 4

B

x \in [- 4; - 3]

C

x \in (- 4; - 3)

D

x \in \emptyset

Question 4: Solve the inequality:

|x^{2} - 3 x + 6| \leq 6

A

x \in [0; 3)

B

x \in (0; 3)

C

х \in ℝ

D

x \in [0; 3]

Question 5: Solve the inequality:

\sqrt{x^{2} - 3 x - 10} < x

A

x \in (- \infty; - 2] \cup [5; + \infty)

B

x \in (- \frac{10}{3}; 2]

C

x \in (- \infty; - \frac{10}{3}]

D

x \in (- \infty; - \frac{10}{3})

Question 6: Solve the inequality:

\frac{x^{2} - 9 x + 20}{x^{2} - 6 x + 8} < 0

A

x \in (2; 5)

B

x = 4

C

x \in [2; 5] \ \{4\}

D

x \in (2; 5) \ \{4\}

Question 7: Solve the inequality:

\frac{1}{x + 3} > \frac{1}{x - 1}

A

x \in (1; + \infty)

B

x \in (- \infty; - 3) \cup (1; + \infty)

C

x \in (- 3; 1)

D

x \in (- \infty; - 3)

Question 8: Solve the inequality:

\frac{x^{2} - 4 x - 5}{x^{2} - 11 x + 30} > 0

A

x \in (- 1; 5) \cup (6; + \infty)

B

x \in (6; + \infty)

C

x \in (- \infty; - 1) \cup (6; + \infty)

D

x \in (- \infty; - 1)

Question 9: Solve the inequality:

\frac{x^{2} - 4 x + 4}{x - 1} > 0

A

x \in (1; 2) \cup (2; + \infty)

B

x \in (2; + \infty)

C

x \in (- 1; - 2)

D

x \in (- 1; + \infty)

Question 10: Solve the inequality:

\frac{{(\sqrt{x})}^{2} + 20 - x^{2}}{x + 1} \leq 0

A

x \in [- 4; - 1] \cup [5; + \infty)

B

x \in [- 4; - 1) \cup [5; + \infty)

C

x \in (5; + \infty)

D

x \in [5; + \infty)

Test: Inequalities II - Challenging

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