Question

Rezolvati in multimea Z ecuatia
a) |x|=18
b) |x| =-2
c) |2x-3|=7
d) |5-8x|=35
Va rog frumos URGENT!!!!!

Answer 1

|x|=18⇒x=18 , -18

|x| =-2  ( F) ⇒ x= ∅

|2x-3|=7
2x-3=7        2x-3=-7
2x=10        2x=-4
x=10:2        x=(-4) : 2
x=25         x=-2
x=-2,5

|5-8x|=35         
5-8x=-35     
8x=40             
x=40 : 8
x=5

Answer 2

$\displaystyle a).|x|=18 \Rightarrow x=18\\ \\ ~~~~~~~~~~~~~~~\Rightarrow x=-18$

$\displaystyle b).|x|=-2~(F)$

$\displaystyle c).|2x-3|=7 \\ \\ 2x-3=7 \Rightarrow 2x=7+3 \Rightarrow 2x=10 \Rightarrow x= \frac{10}{2} \Rightarrow x=5 \\ \\ 2x-3=-7 \Rightarrow 2x=-7+3 \Rightarrow 2x=-4 \Rightarrow x=- \frac{4}{2} \Rightarrow x=-2$

$\displaystyle d).|5-8x|=35 \\ \\ 5-8x=35 \Rightarrow -8x=35-5 \Rightarrow -8x=30 \Rightarrow x=- \frac{30}{8} \Rightarrow x=- \frac{15}{4} \not \in Z\\ \\ 5-8x=-35 \Rightarrow -8x=-35-5 \Rightarrow -8x=-40 \Rightarrow x= \frac{40}{8} \Rightarrow x=5$