which is a solution to $(x - 2)(x + 10) = 13$?\n$x = 3$\n$x = 8$\n$x = 10$\n$x = 11$

Explanation:

Step1: Substitute (x = 3) into the equation

Substitute (x = 3) into ((x - 2)(x + 10)): [ \begin{align*} (3-2)(3 + 10)&=1\times13\ &=13 \end{align*} ]

Step2: Substitute (x = 8) into the equation

Substitute (x = 8) into ((x - 2)(x + 10)): [ \begin{align*} (8-2)(8 + 10)&=6\times18\ &=108\neq13 \end{align*} ]

Step3: Substitute (x = 10) into the equation

Substitute (x = 10) into ((x - 2)(x + 10)): [ \begin{align*} (10-2)(10 + 10)&=8\times20\ &=160\neq13 \end{align*} ]

Step4: Substitute (x = 11) into the equation

Substitute (x = 11) into ((x - 2)(x + 10)): [ \begin{align*} (11-2)(11 + 10)&=9\times21\ &=189\neq13 \end{align*} ]

Answer:

(x = 3) (i.e., the first option (x = 3))