Solve (y-5)-6(3+y)=7: Step-by-Step Linear Equation

Let's solve the given linear equation step-by-step:

• Step 1: Distribute the $-6$ across the terms inside the parenthesis:
  The given equation is $(y - 5) - 6(3 + y) = 7$.
  Distribute $-6$ to both $3$ and $y$:
  $-6 \times 3 = -18$ and $-6 \times y = -6y$.
  Rewrite the equation as: $y - 5 - 18 - 6y = 7$.
• Step 2: Combine like terms:
  Combine $y$ and $-6y$ to get $-5y$.
  Combine $-5$ and $-18$ to get $-23$.
  This simplifies the equation to: $-5y - 23 = 7$.
• Step 3: Isolate the variable $y$:
  Add $23$ to both sides to eliminate $-23$:
  $-5y - 23 + 23 = 7 + 23$ simplifies to $-5y = 30$.
  Divide both sides by $-5$ to solve for $y$:
  $y = \frac{30}{-5} = -6$.

Thus, the solution to the equation is $y = -6$.