1. -5(x - 2) - (x + 2) = 50

Explanation:

Step1: Expand the expressions

First, expand (-5(x - 2)-(x + 2)) using the distributive property. (-5(x - 2)=-5x+10) and (-(x + 2)=-x - 2). So the left - hand side becomes (-5x + 10-x - 2).

Step2: Combine like terms

Combine the (x) terms and the constant terms. (-5x-x+10 - 2=-6x + 8). The equation is now (-6x+8 = 50).

Step3: Isolate the variable term

Subtract 8 from both sides of the equation: (-6x+8-8=50 - 8), which simplifies to (-6x=42).

Step4: Solve for (x)

Divide both sides of the equation by (-6): (\frac{-6x}{-6}=\frac{42}{-6}), so (x=-7).

Answer:

(x=-7)