Răspuns:
(a) [tex]\bf x\in[3,4)[/tex]
(b) [tex]\bf x\in[-5, -4)[/tex]
(c) [tex]\bf x\in \Big[1,\dfrac{3}{2}\Big)[/tex]
(d) [tex]\bf x\in \Big[\dfrac{3}{2},\dfrac{11}{6}\Big)[/tex]
Explicație pas cu pas:
Salutare!
(a)
[x] = 3
[tex]\bf 3\leq x < 4[/tex]
[tex]\boxed{\bf x\in[3,4)}[/tex]
(b)
[x + 2] = -3
[tex]\bf -3\leq x+2 <-2\:\:\Big|-2\:\:\:\:\text{\it(Scadem toata relatia cu 2)}[/tex]
[tex]\bf -3-2\leq x+2-2 <-2-2[/tex]
[tex]\bf -5\leq x <-4[/tex]
[tex]\boxed{\bf x\in[-5, -4)}[/tex]
(c)
[2x] = 2
[tex]\bf 2\leq 2x < 3\:\:\Big|:2\:\:\:\:\text{\it(Impartim toata relatia cu 2)}[/tex]
[tex]\bf 1\leq x < \dfrac{3}{2}[/tex]
[tex]\boxed{\bf x\in \Big[1,\dfrac{3}{2}\Big)}[/tex]
(d)
[3x + 1/2 ] = 5
[tex]\bf 5\leq 3x+\dfrac{1}{2} <6\:\:\Big|\cdot2\:\:\:\:\text{\it(Inmultim toata relatia cu 2)}[/tex]
[tex]\bf 5\cdot 2\leq 6x+1 <6\cdot2[/tex]
[tex]\bf 10 \leq 6x+1 < 12\:\:\Big|-1\:\:\:\:\text{\it(Scadem toata relatia cu 1)}[/tex]
[tex]\bf 10 -1\leq 6x+1-1 < 12-1[/tex]
[tex]\bf 9\leq 6x < 11\:\:\Big|:6\:\:\:\:\text{\it(Impartim toata relatia cu 6)}[/tex]
[tex]\bf \dfrac{9}{6}\leq x < \dfrac{11}{6}[/tex]
[tex]\bf \dfrac{\not9}{\not6}\leq x < \dfrac{11}{6}[/tex]
[tex]\bf \dfrac{3}{2}\leq x < \dfrac{11}{6}[/tex]
[tex]\boxed{\bf x\in \Big[\dfrac{3}{2},\dfrac{11}{6}\Big)}[/tex]
==pav38==
