Question

Fie s si y apartin lui R a.î. |3y-2x-6|<=5 si |3x-4y+1<=2. Sa se arate ca -12<=y-x<=2.

Answer 1

$|3y-2x-6|\leq 5\leftrightarrow -5\leq 3y-2x-6\leq 5\\|3x-4y+1|\leq 2\leftrightarrow -2\leq3x-4y+1\leq2\\\text{Adun\u am cele dou\u a}\\-7\leq-y+x-5\leq7\\\text{Adun\u am 5}\\-2\leq-y+x\leq12\\\text{\^Inmul\c tim cu (-1)}\\-12\leq y-x\leq2$