Question

1. -r - 2(6r - 5)= - 81

Explanation:

Step1: Expand the expression

First, expand $-2(6r - 5)$ using the distributive - property $a(b - c)=ab - ac$. Here, $a=-2$, $b = 6r$, and $c = 5$. So, $-2(6r - 5)=-12r+10$. The original equation $-r-2(6r - 5)=-81$ becomes $-r-12r + 10=-81$.

Step2: Combine like - terms

Combine the $r$ terms on the left - hand side. $-r-12r=-13r$. The equation is now $-13r + 10=-81$.

Step3: Isolate the variable term

Subtract 10 from both sides of the equation. $-13r+10 - 10=-81 - 10$. This simplifies to $-13r=-91$.

Step4: Solve for $r$

Divide both sides of the equation by $-13$. $\frac{-13r}{-13}=\frac{-91}{-13}$. So, $r = 7$.

Answer:

$r = 7$