Absolute value equations and inequalities

2000002201

Level:

Identify the solution set of the following inequality.

| 2 x + 5 | > 0

R ∖ {- 2.5}

\emptyset

(- 2.5; \infty)

(- \infty; - 2.5)

Level:

Choose the equation that has only one solution.

- | x - 3 | = 0

| x - 3 | + 1 = 0

| x - 3 | = 3

3 + | x - 3 | = 0

Level:

Choose the equation that has no solution.

| 3 x - 5 | = - 1

| 3 x - 5 | = 0

| 3 x - 5 | = 1

3 | x + 5 | = 0

Level:

Choose the equation that has only positive solutions.

| x - 5 | = 3

| x - 3 | = 5

| x - 2 | = 2

| x + 10 | = 8

Level:

Find the solution set of the equation

| x - 1 | = 12

{- 11; 13}

{- 13; 11}

{- 11}

{13}

Level:

Find the solution set of the equation

| x + 1 | = 0

{- 1}

\emptyset

{- 1; 1}

{1}

Submitted by ladislav.foltyn on Sat, 03/02/2019 - 16:24

Level:

Find the sum of all the roots of the equation

| x + 4 | = | 2 x - 7 |

12

11

- 11

23

Level:

Find the number of the roots of the equation

| x + 3 | + | x + 2 | = 6

2

1

4

3

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