Question

(2x-3)^2>25.

(2x+7)^2≤169 ​

Answer 1

1)$(2x-3)^{2} >25\rightarrow \left[\begin{array}{cc}(2x-3)>5\\(2x-3)<-5\end] \rightarrow \left[\begin{array}{cc}2x>8\\2x<-2\end] \rightarrow \left[\begin{array}{cc}x>4\\x<-1\end]$

Ответ: $x\in(-\infty;-1)\cup(4;+\infty)$

2)$(2x+7)^{2}\leq169\rightarrow \left[\begin{array}{cc}(2x+7)\leq13\\(2x+7)\geq-13\end] \rightarrow\left[\begin{array}{cc}2x\leq6\\2x\geq-20\end] \rightarrow\left[\begin{array}{cc}x\leq3\\x\geq-10\end]$

Ответ:$x\in[-10;3]$