Solve the equation. \[ 7(3 x+6)=11-(x+2) \]

Step 1 ：Distribute the 7 on the left side of the equation to get \(21x + 42\).

Step 2 ：Simplify the right side of the equation to get \(9 - x\).

Step 3 ：Set the two expressions equal to each other: \(21x + 42 = 9 - x\).

Step 4 ：Combine like terms to get the simplified equation \(x = -\frac{3}{2}\).

Step 5 ：Substitute \(x = -\frac{3}{2}\) back into the original equation to verify that both sides of the equation are equal.

Step 6 ：Final Answer: The solution to the equation is \(\boxed{-\frac{3}{2}}\).