Question

9 rezolvati in multimea numerelor intregi ecuatiile
a. 2(4x+5)=-3x+32
b. 3(-2x+7)=-5x+23
c. -3(-x+1)=3x-3
d. -2(x-4)+6=-4x+5(x-2)
e. 5-3(x+2)=2x+3(x+5)
f. 5+4(1-x)=3x+9​

Answer 1

Explicație pas cu pas:

a)

$2(4x+5)=-3x+32 \\ 8x + 10 = - 3x + 32 \\ 8x + 3x = 32 - 10 \\ 11x = 22 = > x = 2$

b)

$3(-2x+7)=-5x+23 \\ - 6x + 21 = - 5x + 23 \\ - 6x + 5x = 23 - 21 \\ - x = 2 = > x = - 2$

c)

$-3(-x+1)=3x-3 \\ 3x - 3 = 3x - 3 \\ 3x - 3x = - 3 + 3 \\ 0 \cdot x = 0 \implies x \in \mathbb{Z}$

d)

$-2(x-4)+6=-4x+5(x-2) \\ - 2x + 8 + 6 = - 4x + 5x - 10 \\ - 2x + 14 = x - 10 \\ - 2x - x = - 10 - 14 \\ - 3x = - 24 \implies x = 8$

e)

$5-3(x+2)=2x+3(x+5) \\ 5 - 3x - 6 = 2x + 3x + 15 \\ - 3x - 1 = 5x + 15 \\ - 3x - 5x = 15 + 1 \\ - 8x = 16 \implies x = - 2$

f)

$5+4(1-x)=3x+9 \\ 5 + 4 - 4x = 3x + 9 \\ 9 - 4x = 3x + 9 \\ - 4x - 3x = 9 - 9 \\ - 7x = 0 \implies x = 0$