Solve the following inequality for d*d*. Write your answer in simplest form.

6, d, plus, 2, is greater than or equal to, d, minus, 9

6*d*+2≥

*d*−9

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.

Solve the following inequality for d. Write your answer in simplest form: 6d + 2 ≥ d - 9.

Learn how to solve the linear inequality 6d + 2 ≥ d - 9 step by step. This problem covers key concepts of algebra and inequalities, demonstrating how to isolate the variable d and solve for the simplest form. Suitable for students in Grades 6-8.

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