Question

Aflati cel mai mare număr m apartine lui Q, pentru care x = -3 este solutie a inecuatiei 3x - 2m(x-1)<_ 1- 5(x+m) , <_ =(mai mic sau egal)

Answer 1

$3x-2m(x-1) \leq 1-5(x+m) \\ \\ x=-3 \Rightarrow -9-2m \cdot (-4) \leq 1-5(-3+m) \\ \\ -9+8m \leq 1+15-5m \\ \\ 8m+5m \leq 1+15+9 \\ \\ 13m \leq 25 \\ \\ m \leq \frac{25}{13} \Rightarrow Cel~mai~mare~numar~m~este~ \frac{25}{13}.$

Answer 2

 3x-2m(x-1) \leq 1-5(x+m) \\  \\ x=-3 \Rightarrow  -9-2m \cdot (-4) \leq 1-5(-3+m) \\  \\ -9+8m \leq 1+15-5m \\  \\ 8m+5m \leq 1+15+9 \\  \\ 13m \leq 25 \\  \\ m \leq  \frac{25}{13} \Rightarrow Cel~mai~mare~numar~m~este~ \frac{25}{13}.