Question

8. Rezolvaţi în Z ecuațiile: a) 2(x - 1) = 3(x + 1) - 6; c) 2(1 + x) = 3x; b) 3(2x - 1) = 4(x − 2) + 15; d) 73(x+2) = 2x - 19; e) 2(x + 4) = x + 7; f) 5(x + 9) = 6(x + 8); g) 7(x - 1)-2(x + 1) = 2 (x + 3); h) 2(2x + 2) + 6(x − 1) = 4(x + 1). Vă rog​

Answer 1

Explicație pas cu pas:

a)

$2(x - 1) = 3(x + 1) - 6 \\ 2x - 2 = 3x + 3 - 6 \\ 2x - 3x = - 3 + 2 \\ - x = - 1 \\ x = 1$

b)

$3(2x - 1) = 4(x − 2) + 15 \\ 6x - 3 = 4x - 8 + 15 \\ 6x - 4x = 7 + 3 \\ 2x = 10 \\ x = 5$

c)

$2(1 + x) = 3x \\ 2 + 2x = 3x \\ 2x - 3x = - 2 \\ - x = - 2 \\ x = 2$

d)

$73(x+2) = 2x - 19 \\ 73x + 146 = 2x - 19 \\ 73x - 2x = - 19 - 146 \\ 71x = - 165 \\ x = - \frac{165}{71}$

sau

$3(x+2) = 2x - 19 \\ 3x + 6 = 2x - 19 \\ 3x - 2x = - 19 - 6 \\ - x = - 25 \\ x = 25$

e)

$2(x + 4) = x + 7 \\ 2x + 8 = x + 7 \\ 2x - x = 7 - 8 \\ x = - 1$

f)

$5(x + 9) = 6(x + 8) \\ 5x + 45 = 6x + 48 \\ 5x - 6x = 48 - 45 \\ - x = 3 \\ x = - 3$

g)

$7(x - 1)-2(x + 1) = 2 (x + 3) \\ 7x - 7 - 2x - 2 = 2x + 6 \\ 5x - 2x = 6 + 9 \\ 3x = 15 \\ x = 5$

h)

$2(2x + 2) + 6(x − 1) = 4(x + 1) \\ 4x + 4 + 6x - 6 = 4x + 4 \\ 10x - 4x = 4 + 2 \\ 6x = 6 \\ x = 1$