Question

1. solve for x. -2(-x - 4) - 3x - 5 = -5

Explanation:

Step1: Expand the left - hand side

First, expand $-2(-x - 4)$ using the distributive property $a(b + c)=ab+ac$. Here $a=-2$, $b=-x$ and $c = - 4$. So $-2(-x - 4)=(-2)\times(-x)+(-2)\times(-4)=2x + 8$. The equation becomes $2x + 8-3x - 5=-5$.

Step2: Combine like terms

Combine the $x$ - terms and the constant terms on the left - hand side. $(2x-3x)+(8 - 5)=-5$, which simplifies to $-x+3=-5$.

Step3: Isolate the variable term

Subtract 3 from both sides of the equation. $-x+3 - 3=-5 - 3$, resulting in $-x=-8$.

Step4: Solve for x

Multiply both sides by - 1 to get $x = 8$.

Answer:

$x = 8$