How many solutions are there for the absolute value equation "| 16 + t | = 2t - 3"?

Hello:

| 16 + t | = 2t - 3 ... (*)

note 1 : if (a = b) so : (a² = b²)

note 2 : | a |² = a²

note 3 : a² - b² = (a+b) (a - b)

(*); (16+t) ² = (2t - 3) ²

(16+t) ² - (2t - 3) ² = ((16+t) + (2t - 3)) ((16+t) - (2t - 3)) = 0

(6t + 13) ( - t + 19) = 0

6t+13 = 0 t = - 13/6

- t + 18 = 0 t = 19

verif : t = 19 : | 16 + 19 | = 2 (19) - 3 : 35 = 35 ... (right)

t = - 13/6 : | 16 + (-13/6) | = 2 (-13/6) - 3

| 16 + (-13/6) | = - 13/3 - 3 < 0 no solution because the absolute value is positif

conclusion : one solution : 19