Question

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

Answer 1

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