Absolute value

1003124208

Level:

Assuming

- 6 < x < 0

, the expression

\frac{| x + 6 | - x + 6}{x}

is equal to:

\frac{12}{x}

- \frac{12}{x}

2

0

1003124209

Level:

Which of the given inequalities holds for

x = 2 π

| x + 1 | > 5

| x - 1 | < 2

| x + 3 | \leq 4

| x - 5 | \geq 3

1003124210

Level:

Which two numbers do both satisfy the equation

| 3 x - 3 | = 9

- 2, 4

- 4, 2

- 5, 7

- 7, 5

1003187001

Level:

Let

x \in (- \infty; - 4]

. The value of the expression

| | x | - 4 | - 2 | x - 4 | + | 10 - x |

is equal to:

- 2

- 6

2

6

1003187003

Level:

Simplifying the expression

| 3 x - 9 | - | 9 - 3 x | + | - 3 x | - | - 9 |

for

x \in [3; 9]

you get:

3 x - 9

- 3 x + 9

9 x - 27

3 x + 9

1003187004

Level:

Let

x \in (- \infty; 0)

. The expression

| x - | x | | + | x + | x | | + 1 - x | x |

is equal to:

(x - 1)^{2}

(x + 1)^{2}

x^{2} + 1

1 - x^{2}

1003187104

Level:

Let

a

be a positive real number. Then

| x | \leq a

if and only if

- a \leq x \leq a

if and only if

x \leq a

if and only if

x \geq - a

if and only if

x < 0

1003187105

Level:

Let

a

be a positive real number. Then

| x | \geq a

if and only if

x \geq a

x \leq - a

if and only if

x \geq a

if and only if

x \leq - a

if and only if

x > 0

1003187304

Level:

How many solutions does the equation

| | x - 4 | - 2 | + 2 = 0

have?

0

2

4

6

1003187405

Level:

Choose the expression which takes only negative values.

- | 2 - 4 x | - 1

| - 2 x - 5 | - 2

- | 2 - 4 x | + 2

| 2 - x | - 2

1003124208

1003124209

1003124210

1003187001

1003187003

1003187004

1003187104

1003187105

1003187304

1003187405

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