Question

|10-| x-3 || = 6
va rog, dau coroană ​

Answer 1

Răspuns:

Explicație pas cu pas:

10-|x-3|=6

4=|x-3|

x-3=4........x=7

x-3=-4...............x=-1

10-|x-3|=-6

16=|x-3|

x-3=16.........x=19

x-3=-16.......x=-13

S={-13;-1;7;19}

atasezezolvarea grafica pt verificare

Answer 2

$\it |10-|x-3||=6 \Rightarrow 10-|x-3|=\pm6 \Rightarrow |x-3|-10=\pm6 \Rightarrow \\ \\ \Rightarrow |x-3|-10\in\{-6,\ 6\}\bigg|_{+10} \Rightarrow |x-3|\in\{4,\ \ 16\} \Rightarrow x-3\in\{\pm4,\ \ \pm16\} \Rightarrow \\ \\ \Rightarrow x-3\in\{-16,\ -4,\ 4,\ 16\}\bigg|_{+3} \Rightarrow x\in\{-13,\ \ -1,\ \ 7,\ \ 19\}$