Question

5+2•3:|2-X| = 14

6+2•|4-2(X+1)| = 4x​

Answer 1

$\it 5+2\cdot3|2-x|-14 \Rightarrow 5+6\cdot|2-x|=14|_{-5} \Rightarrow 6\cdot|2-x|=9|_{:6} \Rightarrow \\ \\ \Rightarrow |2-x|=\dfrac{\ 9^{(3}}{6} \Rightarrow |2-x|=\dfrac{3}{2} \Rightarrow |x-2|=1,5 \Rightarrow x-2=\pm1,5 \Rightarrow \\ \\ x-2\in\{-1,5;\ 1,5\}|_{+2} \Rightarrow x\in\{0,5;\ 3,5\}$

$\it \rule{100}{0.4}\\ \\6+2|4-2(x+1)|=4x \Rightarrow 2|4-2x-2|=4x-6|_{:2} \Rightarrow|2-2x| =2x-3 \Rightarrow \\ \\ \Rightarrow |2x-2|=2x-3\\ \\ Vom\ nota\ 2x-2=t,\ iar\ ultima\ ecua\c{\it t}ie\ devine:\\ \\ |t|=t-1\ \ \ \ \ (*)\\ \\ I)\ t<0\stackrel{(*)}{\Longrightarrow} -t=t-1 \Rightarrow -2t=-1|_{\cdot{(-1)}} \Rightarrow 2t=1 \Rightarrow t=\dfrac{1}{2}>0\ nu\ convine\\ \\ II)\ t>0 \stackrel{(*)}{\Longrightarrow} t=t-1 \Rightarrow t-t=-1 \Rightarrow 0t=-1 \Rightarrow t\in\varnothing$

Deci, ecuația nu admite nici o soluție.