Absolute value equations and inequalities

1003162904

Level:

Find the sum of all the roots of the equation

| | 1 - x | - 2 | = 1

for

x \in (1; \infty)

6

4

1

2

1003162903

Level:

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

| | x - 4 | - 2 | = 0

8

12

4

6

1003162902

Level:

Calculate for which value(s) of the parameter

t

the given equation has no solution.

| x + 4 | - 2 = t

t \in (- \infty; - 2)

t \in (- \infty; - 4)

t \in (- 4; \infty)

t \in (- \infty; 2)

1003162901

Level:

Calculate for which value(s) of the parameter

t

the given equation has at least one solution.

| x - 5 | = t

t \in [0; \infty)

t \in [5; \infty)

t \in {0}

t \in (- \infty; 5]

1003163005

Level:

Find all

t

t \in R

, such that the following equation with the variable

x

has exactly two solutions.

| x - t | + 1 = 3

t \in R

t \in (- \infty; 2)

t \in (2; \infty)

t \in (- 2; \infty)

1003163004

Level:

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

| | x - 4 | - 9 | = 0

8

18

6

4

1003163003

Level:

How many roots has the given equation for

x \in (- \infty; - 3]

| 3 - 2 x | - 3 | x | = - 8

1

2

0

3

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]

1003163001

Level:

Find all

t

t \in R

, such that the following equation with the variable

x

has exactly two solutions.

| x | + t = - 3

t \in (- \infty; - 3)

t \in {- 3}

t \in (- 3; \infty)

t \in {- 3; 3}

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

Absolute value equations and inequalities

1003162904

1003162903

1003162902

1003162901

1003163005

1003163004

1003163003

1003163002

1003163001

1003177805

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