Rational equations and inequalities | math4u.vsb.cz

9000021810

Level:

B

Find all the values of

x

for which the following expression takes on values smaller than or equal to

1

.

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

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

x \in (- \infty; - 3]

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

x \in [- 3; - 1)

9000022804

Level:

B

Establish the values of the real parameter

t

which ensure that the following expression is nonpositive.

\frac{2}{2 t^{2} + t - 1}

(- 1; \frac{1}{2})

[- \frac{1}{2}; 1]

[- 1; \frac{1}{2}]

(- \frac{1}{2}; 1)

9000026106

Level:

B

Find the solution set of the following inequality.

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

(1; \infty)

(- \infty; 1)

(- \infty; 3]

[3; \infty)

9000026108

Level:

B

An inequality is solved graphically as shown in the picture. The solution is marked in red. Choose the corresponding inequality.

2 \leq \frac{x + 3}{x}

2 \geq \frac{3}{x}

2 \geq \frac{x + 3}{x}

2 \leq \frac{3}{x}

9000033304

Level:

B

Find the solution set of the following inequality.

\frac{x + 4}{x + 2} \leq 0

[- 4; - 2)

(- \infty; - 4] \cup [2; \infty)

(- \infty; - 4) \cup (- 2; \infty)

(- 4; - 2]

9000033305

Level:

B

Find the solution set of the following inequality.

\frac{2}{x + 1} \geq 1

(- 1; 1]

[- 1; 1)

(- \infty; - 1) \cup [1; \infty)

(- \infty; 1]

9000033306

Level:

B

Find the solution set of the following inequality.

\frac{2}{3} < \frac{2 + x}{3 + x}

(- \infty; - 3) \cup (0; \infty)

R

(- 3; \infty)

(- 3; 0)

9000033307

Level:

B

Find the solution set of the following inequality.

\frac{4}{x^{2} - x - 6} \leq 0

(- 2; 3)

R

(- \infty; - 2) \cup (3; \infty)

(- 3; 2)

9000039005

Level:

B

Find all the values of

x

for which the following expression is positive.

\frac{2 x - 3}{7 - 3 x}

x \in (\frac{3}{2}; \frac{7}{3})

x \in (\frac{3}{2}; + \infty)

x \in (\frac{7}{3}; + \infty)

x \in (0; + \infty)

9100033310

Level:

B

Identify the picture that shows the correct solution set of the following inequality. In each picture, the set of points corresponding to the solution set is marked in red.

\frac{x}{x - 1} < 0