|2x + (5/3)| < 1 → the contents of an absolute value can be positive or negative

- 1 < 2x + (5/3) < 1 → you subtract (5/3) both sides

- 1 - (5/3) < 2x + (5/3) - (5/3) < 1 - (5/3) → you simplify

- (3/3) - (5/3) < 2x < (3/3) - (5/3) → you simplify

- 8/3 < 2x < - 2/3 → you divide by 2 both sides

- 8/6 < x < - 2/6 → you simplify

- 4/3 < x < - 1/3

Hola

Vamos a suponer

|(2 x + 5 )/ 3| < 1

Tenemos 2 caminos

1º camino

(2 x + 5 )/ 3 < 1

Multiplicamos todo por 3

2 x + 5 < 3*1

2 x + 5 < 3

Restamos 5 a todo

2 x < 3 - 5

2 x < -2

Dividimos todo por 2

x < -2/2

x < -1

**********

2º camino

(2 x + 5 )/ 3 > -1

Multiplicamos todo por 3

2 x + 5 > 3*-1

2 x + 5 > -3

Restamos 5 a todo

2 x > -3 - 5

2 x > -8

Dividimos todo por 2

x > -8/2

x > -4

**********

Con los 2 caminos tenemos

-4 < x < -1

ó en intervalos

x € (-4 ; -1)

**********

Saludos

Ni **** idea

http://es.symbolab.com/solver/absolute-inequalitie...