Question

Помогите,пожалуйста. Сумма целых решений неравенства 14-|4x-5|⩾3 равна

Answer 1

|4x-5|<=11
-11 <= 4x-5 <=11
-6 <= 4x <= 16
-1.5 <= x <= 4
x=-1;0;1;2;3;4
suma=9

Answer 2

$14-|4x-5| \geq 3\\\\|4x-5| \leq 11\\\\a)\quad 4x-5 \geq 0,\; \; x \geq \frac{5}{4}\quad \Rightarrow \; \; 4x-5 \leq 11\\\\4x \leq 16\\\\x \leq 4\\\\x\in [\, \frac{5}{4};4\, ]\\\\Celue:\; \; 2,\; 3,\; 4\; .\\\\b)\quad 4x-5\ \textless \ 0\; ,\; \; x\ \textless \ \frac{5}{4}\quad \Rightarrow \; \; -(4x-5) \leq 11\\\\-4x+5 \leq 11\; ,\; \; 4x \geq -6\\\\x \geq -\frac{3}{2}\\\\x\in [-\frac{3}{2};\frac{5}{4})\\\\Celue:\; \; -1,\; 0,\; 1\; .\\\\c)\quad Summa:\; \; 2+3+4-1+1=9$