To solve the inequality $6d + 2 \geq d - 9$, follow these steps:

Step 1: Move all the terms involving $d$ to one side of the inequality.

Subtract $d$ from both sides:

$6d + 2 - d \geq d - 9 - d$

This simplifies to:

$5d + 2 \geq -9$

Step 2: Move the constant terms to the other side of the inequality.

Subtract 2 from both sides:

$5d + 2 - 2 \geq -9 - 2$

This simplifies to:

$5d \geq -11$

Step 3: Solve for $d$.

Divide both sides by 5:

$d \geq \frac{-11}{5}$

So, the solution is:

$d \geq -\frac{11}{5}$

This is the simplest form of the solution.

Do you need further details or have any questions?

Here are 5 related questions:

1. How do you solve inequalities that involve multiplication or division by a negative number?
2. What is the difference between solving an equation and solving an inequality?
3. Can you explain how to graph the solution $d \geq -\frac{11}{5}$?
4. How would the inequality change if we had $6d + 2 \leq d - 9$?
5. Can you provide examples of inequalities with fractions?

Tip: Always remember, when multiplying or dividing an inequality by a negative number, reverse the inequality sign.