Absolute value equations and inequalities

2010008601

Level:

Choose the equation which is, on the interval

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

, equivalent to

| 2 x - 1 | + 2 | x + 5 | = 1 - | 2 - x | .

(2 x - 1) + 2 (x + 5) = 1 - (2 - x)

(2 x - 1) + 2 (x + 5) = 1 + (2 - x)

(2 x - 1) - 2 (x + 5) = 1 + (2 - x)

- (2 x - 1) + 2 (x + 5) = 1 + (2 - x)

2010008505

Level:

Give the solution set of the equation

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

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

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

[- 2; + \infty)

[4; + \infty)

2010008504

Level:

Give the number which satisfies the equation

| x + 2 | - 1 = x + 3

- 3

- 2

0

1

2010008503

Level:

Choose the equation which has only one solution.

5 - | 2 x + 2 | - 1 = 4

5 - | 2 x + 2 | + 1 = 5

- | 2 x + 2 | + 3 = 4

- | 2 x + 2 | + 1 = 0

2010008502

Level:

Find all

t \in R

, such that the following equation with the variable

x

has more than two solutions.

| 1 - | 2 - x | | + 1 = t

t \in (1; 2]

t \in {2}

t \in (2; \infty)

t \in \emptyset

2010008501

Level:

Find all

t \in R

, such that the following equation with the variable

x

has exactly two solutions.

| x + 2 | + 3 = t - 1

t \in (4; \infty)

t \in (- 2; \infty)

t \in {4}

R

2000002205

Level:

Identify the solution set of the following inequality.

| 7 x + 1 | + 1 > 0

R

\emptyset

R ∖ {\frac{1}{7}}

R ∖ {- \frac{1}{7}}

2000002204

Level:

Identify the solution set of the following inequality.

- | 2 x - 100 | < 0

R ∖ {50}

R

R ∖ {- 50}

{50}

2000002203

Level:

Identify the solution set of the following inequality.

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

\emptyset

R

R ∖ {- 3; - 2}

{- 3; - 2}

2000002202

Level:

Identify the solution set of the following inequality.

| x - 25 | \leq 0

{25}

\emptyset

R ∖ {25}

(- \infty; - 25)

Absolute value equations and inequalities

2010008601

2010008505

2010008504

2010008503

2010008502

2010008501

2000002205

2000002204

2000002203

2000002202

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