Solve (question no. 2-22) for x :

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

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

⇒ x(x + 6) - 1(x + 6) - x(x - 3) + 2(x - 3) = 3

⇒ x² + 6x - 1x - 6 - x² + 3x + 2x - 6 = 3

⇒ x² - x² + 6x - 1x + 3x + 2x - 6 - 6 = 3

⇒ 10x - 12 = 3

⇒ 10x = 3 + 12

⇒ 10x = 15

⇒ x = $\dfrac{15}{10}$

⇒ x = $\dfrac{3}{2}$

⇒ x = $1\dfrac{1}{2}$

Hence, the value of x is $1\dfrac{1}{2}$.