Question

x² - 2x - 8 < 7 |x - 4|​

Answer 1

Объяснение:

$x^2-2x-8<7*|x-4|\\x^2-4x+2x-8-7*|x-4|<0\\x*(x-4)+2*(x-4)-7*|x-4|<0\\(x-4)*(x+2)-7*|x-4|<0\\1.\ x-4<0\ \ \ \Rightarrow\ \ \ x<4\\(x-4)*(x+2)-7*(-(x-4))<0\\(x-4)*(x+2)+7*(x-4)<0\\(x-4)*(x+2+7)<0\\(x-4)*(x+9)<0.$

-∞__+__-9__-__4__+__+∞

x∈(-9;4).

$2.\ x-4>0\ \ \ \Rightarrow\ \ \ x>4\\(x-4)*(x+2)-7*(x-4)<0\\(x-4)*(x+2)-7*(x-4)<0\\(x-4)*(x+2-7)<0\\(x-4)*(x-5)<0.$

-∞__+__4__-__5__+__+∞

x∈(4;5).

$3.\ x=4\\(4-4)*(4+2)-7*|4-4|<0\\0*6-7*0<0\\0<0\ \ \ \Rightarrow\ \ \ x\neq 4.$

Ответ: x∈(-9;4)U(4;5).