Absolute value equations and inequalities

1003162905

Level:

Choose the equation that is equivalent to

| | 2 - x | - 1 | = 1

for

x \in (3; \infty)

(x - 2) - 1 = 1

- (x - 2) - 1 = 1

- (1 - (2 - x)) = 1

1 - (x - 2) = 1

1003163002

Level:

Find all

t

t \in R

, such that the following equation with the variable

x

has more than two solutions.

| | 3 - x | - 3 | = t

t \in (0; 3]

t \in {0; 3}

t \in {3}

t \in [1; 3]

1003163004

Level:

Find the sum of all the roots of the given equation.

| | x - 4 | - 9 | = 0

8

18

6

4

1003177804

Level:

Choose the solution set of the given inequality.

| | x - 5 | + 2 | > 3

(- \infty; 4) \cup (6; \infty)

(- \infty; - 4) \cup (6; \infty)

(6; \infty)

(- \infty; - 5) \cup (6; \infty)

1003177805

Level:

Let

x \in Z

. Find the sum of all the solutions of the given inequality.

| | | x + 1 | + 1 | + 1 | \leq 3

- 3

- 2

- 4

0

1003187302

Level:

The equation

| | 2 x - 8 | - 4 | = 4

has:

three real solutions

one real solution

four real solutions

two real solutions

1003187401

Level:

Give the solution set of the equation

| | x - 1 | - | 3 - x | | = 2

(- \infty; 1] \cup [3; + \infty)

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

R

(1; 3)

1003187403

Level:

How many solutions does the equation

| | 2 x + 6 | - 8 | = 4

have?

4

2

0

6

1003187410

Level:

How many integers are in the solution set of the given inequalities?

| \sqrt{17} - 2 x | \leq 5 and | 2 x - \sqrt{17} | \leq 5

5

4

6

7

2000002203

Level:

Identify the solution set of the following inequality.

| x + 2 | + | x + 3 | \leq 0

\emptyset

R

R ∖ {- 3; - 2}

{- 3; - 2}

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Absolute value equations and inequalities

1003162905

1003163002

1003163004

1003177804

1003177805

1003187302

1003187401

1003187403

1003187410

2000002203

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