Ответ:

x=-4

---------------&&&&-

Решение:

|x + 3| - |x - 5| = 3x + 4

|x + 3| = 3x + 4 + |x - 5|

====================== #1

x + 3 = 3x + 4 + |x - 5|

-|x - 5| = 3x + 4 - x - 3

-|x - 5| = 2x + 1

=========== #1.1

-x + 5 = 2x + 1

4 = 3x

x₁ = 4/3

=========== #1.2

-x + 5 = -2x - 1

x₂ = -6

====================== #2

x + 3 = -3x - 4 - |x - 5|

|x - 5| = -3x - 4 - x - 3

|x - 5| = -4x - 7

=========== #2.1

x - 5 = -4x - 7

5x = -2

x₃ = -0,4

=========== #2.2

x - 5 = 4x + 7

3x = -12

x₄ = -4

Результаты:

x₁ = 4/3 ∈ ∅

x₂ = -6 ∈ ∅

x₃ = -0,4 ∈ ∅

x₄ = -4

Ответ:

x₁ = -4