Solve the Linear Equation: 6(5+2x)=3x-6 Step by Step

To solve the equation $6\cdot(5+2x)=3x-6$, we will proceed as follows:

• Step 1: Distribute the 6 within the parentheses on the left side:
  $6\cdot(5+2x) = 30 + 12x$.
• Step 2: Substitute the distributed expression into the equation:
  $30 + 12x = 3x - 6$.
• Step 3: Isolate the variable terms on one side:
  Subtract $3x$ from both sides: $30 + 12x - 3x = -6$, which simplifies to $30 + 9x = -6$.
• Step 4: Isolate the term containing $x$:
  Subtract 30 from both sides: $9x = -6 - 30$, which simplifies to $9x = -36$.
• Step 5: Solve for $x$ by dividing both sides by 9:
  $x = \frac{-36}{9} = -4$.

Therefore, the solution to the equation is $x = -4$, which corresponds to choice 1.