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

1 answer:

3 0

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

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