Question

Să se rezolve în mulțimea numerelor naturale ecuația:
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Answer 1

a)

1 + { 2 · [ 3 + ( x - 4 ) · 5 ] : 6 } · 7 = 8

{ 2 · [ 3 + ( x - 4 ) · 5 ] : 6 } · 7 = 8 - 1

{ 2 · [ 3 + ( x - 4 ) · 5 ] : 6 } · 7 = 7

2 · [ 3 + ( x - 4 ) · 5 ] : 6 = 7 : 7

2 · [ 3 + ( x - 4 ) · 5 ] : 6 = 1

2 · [ 3 + ( x - 4 ) · 5 ] = 1 · 6

2 · [ 3 + ( x - 4 ) · 5 ] = 6

3 + ( x - 4 ) · 5 = 6 : 2

3 + ( x - 4 ) · 5 = 3

( x - 4 ) · 5 = 3 - 3

( x - 4 ) · 5 = 0

x - 4 = 0 : 5

x - 4 = 0

x = 0 + 4

x = 4

Answer 2

$1+\left\{2\cdot \left[3+\left(x-4\right)\cdot 5\right]:6\right\}\cdot 7 = 8 \\ \\ \left\{2\cdot \left[3+\left(x-4\right)\cdot 5\right]:6\right\}\cdot 7 = 8-1\\ \\ \left\{2\cdot \left[3+\left(x-4\right)\cdot 5\right]:6\right\}\cdot 7= 7\\ \\ 2\cdot \left[3+\left(x-4\right)\cdot 5\right]:6 = 7:7 \\ \\ 2\cdot \left[3+\left(x-4\right)\cdot 5\right]:6 = 1\\ \\ 2\cdot \left[3+\left(x-4\right)\cdot 5\right] = 1\cdot 6 \\ \\ 3+\left(x-4\right)\cdot 5 = 6:2 \\ \\ 3+\left(x-4\right)\cdot 5 = 3$

$\left(x-4\right)\cdot 5 =3-3\\ \\ \left(x-4\right)\cdot 5 = 0 \\ \\ x-4 = 0:5\\ \\ x-4 = 0\\ \\ \boxed{x = 4}$