Absolute value equations and inequalities

1003047106

Level:

Decide which of the following intervals ensures that the expressions in all the absolute values of the given equation are negative on this interval.

| 5 - x | - | x + 3 | = | x + 1 |

No such interval exists.

(- \infty; - 3)

(- \infty; - 1)

(- 1; 5)

1003047107

Level:

Decide which of the following intervals ensures that the expressions in all the absolute values of the given equation are positive on this interval.

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

(0.5; 1)

(- 4; 1)

(1; \infty)

(- 4; 0)

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]

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)

1003162906

Level:

Find the number of the roots of the equation

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

2

1

4

3

1003162907

Level:

Find the sum of all the roots of the equation

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

12

11

- 11

23

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}

1003163003

Level:

How many roots has the given equation for

x \in (- \infty; - 3]

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

1

2

0

3

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)

1003187303

Level:

Find the solution set of the equation

| x | = - x

(- \infty; 0]

(- 1; 1)

{- 4}

(0; + \infty)

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Absolute value equations and inequalities

1003047106

1003047107

1003162901

1003162902

1003162906

1003162907

1003163001

1003163003

1003163005

1003187303

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