Question

Sa se rezolve :
a) [x]=3
b) [x+2]=-3
c) [2x]=2
d) [3x+1/2]=5

Answer 1

Răspuns:

(a) $\bf x\in[3,4)$

(b) $\bf x\in[-5, -4)$

(c)  $\bf x\in \Big[1,\dfrac{3}{2}\Big)$

(d) $\bf x\in \Big[\dfrac{3}{2},\dfrac{11}{6}\Big)$

Explicație pas cu pas:

Salutare!

(a)

[x] = 3

$\bf 3\leq x < 4$

$\boxed{\bf x\in[3,4)}$

(b)

[x + 2] = -3

$\bf -3\leq x+2 <-2\:\:\Big|-2\:\:\:\:\text{\it(Scadem toata relatia cu 2)}$

$\bf -3-2\leq x+2-2 <-2-2$

$\bf -5\leq x <-4$

$\boxed{\bf x\in[-5, -4)}$

(c)

[2x] = 2

$\bf 2\leq 2x < 3\:\:\Big|:2\:\:\:\:\text{\it(Impartim toata relatia cu 2)}$

$\bf 1\leq x < \dfrac{3}{2}$

$\boxed{\bf x\in \Big[1,\dfrac{3}{2}\Big)}$

(d)

[3x + 1/2 ] = 5

$\bf 5\leq 3x+\dfrac{1}{2} <6\:\:\Big|\cdot2\:\:\:\:\text{\it(Inmultim toata relatia cu 2)}$

$\bf 5\cdot 2\leq 6x+1 <6\cdot2$

$\bf 10 \leq 6x+1 < 12\:\:\Big|-1\:\:\:\:\text{\it(Scadem toata relatia cu 1)}$

$\bf 10 -1\leq 6x+1-1 < 12-1$

$\bf 9\leq 6x < 11\:\:\Big|:6\:\:\:\:\text{\it(Impartim toata relatia cu 6)}$

$\bf \dfrac{9}{6}\leq x < \dfrac{11}{6}$

$\bf \dfrac{\not9}{\not6}\leq x < \dfrac{11}{6}$

$\bf \dfrac{3}{2}\leq x < \dfrac{11}{6}$

$\boxed{\bf x\in \Big[\dfrac{3}{2},\dfrac{11}{6}\Big)}$

==pav38==

Answer 2

Explicație pas cu pas:

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