Đáp án:

Giải thích các bước giải:

Bài `2:`
a) $(x-2)(x+3) - (x+2)(x-7) = -12$
$(x^2 + 3x - 2x - 6) - (x^2 - 7x + 2x - 14) = -12$
$\iff (x^2 + x - 6) - (x^2 - 5x - 14) = -12$
$\iff x^2 + x - 6 - x^2 + 5x + 14 = -12$
$\iff 6x + 8 = -12$
$\iff 6x = -12 - 8$
$\iff 6x = -20$
$\iff x = -\dfrac{20}{6}$
$\iff x = -\dfrac{10}{3}$.
Vậy $x = -\dfrac{10}{3}$.

`b)` $(3x+2)(2x+9) - (x+2)(6x+1) = 3(x-1) - 2(x-6)$
$(6x^2 + 27x + 4x + 18) - (6x^2 + x + 12x + 2) = 3x - 3 - 2x + 12$
$\iff (6x^2 + 31x + 18) - (6x^2 + 13x + 2) = x + 9$
$\iff 6x^2 + 31x + 18 - 6x^2 - 13x - 2 = x + 9$
$\iff 18x + 16 = x + 9$
$\iff 18x - x = 9 - 16$
$\iff 17x = -7$
$\iff x = -\dfrac{7}{17}$.
Vậy $x = -\dfrac{7}{17}$.

`c)` $3(2x-1)(3x-1) - (2x-3)(9x+3) = 0$
$3(6x^2 - 2x - 3x + 1) - (18x^2 + 6x - 27x - 9) = 0$
$\iff 3(6x^2 - 5x + 1) - (18x^2 - 21x - 9) = 0$
$\iff 18x^2 - 15x + 3 - 18x^2 + 21x + 9 = 0$
$\iff 6x + 12 = 0$
$\iff 6x = -12$
$\iff x = -2$.
Vậy $x = -2$.

`d)` $5(3x+5) - 4(2x-3) = 5x + 3(2x+12) + 1$
$15x + 25 - 8x + 12 = 5x + 6x + 36 + 1$
$\iff 7x + 37 = 11x + 37$
$\iff 7x - 11x = 37 - 37$
$\iff -4x = 0$
$\iff x = 0$.
Vậy $x = 0$.

`e)` $4x(5x+2) - (10x-3)(2x+7) = 133$
$20x^2 + 8x - (20x^2 + 70x - 6x - 21) = 133$
$\iff 20x^2 + 8x - (20x^2 + 64x - 21) = 133$
$\iff 20x^2 + 8x - 20x^2 - 64x + 21 = 133$
$\iff -56x + 21 = 133$
$\iff -56x = 133 - 21$
$\iff -56x = 112$
$\iff x = \dfrac{112}{-56}$
$\iff x = -2$.
Vậy $x = -2$.

`g)` $3(6x-5)(4x+1) - (8x+3)(9x-2) = 203$
$3(24x^2 + 6x - 20x - 5) - (72x^2 - 16x + 27x - 6) = 203$
$\iff 3(24x^2 - 14x - 5) - (72x^2 + 11x - 6) = 203$
$\iff 72x^2 - 42x - 15 - 72x^2 - 11x + 6 = 203$
$\iff -53x - 9 = 203$
$\iff -53x = 203 + 9$
$\iff -53x = 212$
$\iff x = \dfrac{212}{-53}$
$\iff x = -4$.
Vậy $x = -4$.