Bài tập theo tuần Toán 8 _ Tuần 32_ đề 1

$\begin{array}{l}a)1+x<3\iff x<2S=\left\{x/x<2\right\}\\ b)2-5x<3\left(2-x\right)\iff 2-5x<6-3x\iff x>-2S=\left\{x/x>-2\right\}\end{array}$

$\begin{array}{l}a)\left|2x-5\right|=4\left(1\right)\\ +)x\ge \frac{5}{2}\Rightarrow \left(1\right)\iff 2x-5=4\iff x=\frac{9}{2}(tm)\\ +)x<\frac{5}{2}\Rightarrow \left(1\right)\iff 5-2x=4\iff x=-\frac{1}{2}(tm)\end{array}$

$\begin{array}{l}b)\frac{5x^2-3x}{5}+\frac{3x+1}{4}<\frac{x\left(2x+1\right)}{2}-\frac{3}{2}\\ \iff \frac{4\left(5x^2-3x\right)+5\left(3x+1\right)}{20}<\frac{10x\left(2x+1\right)-3.10}{20}\\ \iff 20x^2-12x+15x+5<20x^2+10x-30\\ \iff 7x>35\iff x>5\end{array}$

$\left(x-1\right)\left(x-5\right)<0\iff \left[\begin{array}{l}\left\{\begin{array}{l}x-1>0\\ x-5<0\end{array}\right.\\ \left\{\begin{array}{l}x-1<0\\ x-5>0\end{array}\right.\end{array}\right.\iff \left[\begin{array}{l}\left\{\begin{array}{l}x>1\\ x<5\end{array}\right.\\ \left\{\begin{array}{l}x<1\\ x>5\end{array}\right.\end{array}\right.\Rightarrow 1<x<5$