Question

Buna! Ma ajuta cineva cu urmatoarele exercitii?
a) |2x+3|-4|2-(2x+5)|= -27
b) (|x|-1) /4 - (|x|-2 / 4 + 7-2|x|/5 ) = |5x|-5/10 - 7/4
c) 3/2|x - 3/2| = 5/3 |x- 3/2 |- 8/5

Answer 1

a) |2x+3|-4|2-2x-5|=-27 ⇔ |2x+3|-4|-2x-3|=-27 ⇔|2x+3|-4|-(2x+3)|=-27 deoarece  |-x|=|x| ⇒ |2x+3|-4|2x+3|=-27 ⇔ -3|2x+3|=-27 |:(-3)⇔|2x+3|=9 ⇒
1) 2x+3=-9 |-3 ⇔ 2x=-12 |:2 ⇔ x=-6 si 
2) 2x+3= 9 |-3 ⇔ 2x=    6 |:2 ⇔ x=3
b) (|x|-1)/4 - (5|x|/5-2/4+28/4-2|x|/5)=|5|·|x|-1/2-7/4 ⇔(|x|-1)/4-(3|x|/5+26/4)=5|x| -2/4-7/4 ⇔ |x|/4-1/4-3|x|/5-26/4=5|x|-9/4  |+27/4 -5|x| ⇔ |x|/4-3|x|/5-5|x|=18/4  ⇔ 5|x|/20-12|x|/20-100|x|/20=18/4 ⇔ -107|x|/20=90/20 |·20 ⇔ -107|x|=90 ⇔ 
|x|=90:(-107) ⇔ |x|=-90/107 ⇔ x∈Ф (adica ecuatia nu are solutie)
c) 3/2|x-3/2|=5/3|x-3/2|-8/5  |-3/2|x-3/2|+8/5 ⇔ 8/5=5/3|x-3/2|-3/2|x-3/2| ⇔
10/6|x-3/2|-9/6|x-3/2|=8/5 ⇔ 1/6|x-3/2|=8/5  |:1/6 ⇔ |x-3/2|=48/5 ⇒
1) x-3/2=48/5  |+3/2 ⇔x=96/10+15/10 ⇔ x=111/10 si
2) x-3/2=-48/5 |+3/2 ⇔x=-96/10+15/10⇔x=-81/10