Let's solve the equation step by step:

### Given Equation:
\[
2d + 9 - 5d = 2d - 1
\]

### Step 1: Combine like terms on the left side:
\[
(2d - 5d) + 9 = 2d - 1
\]
\[
-3d + 9 = 2d - 1
\]

### Step 2: Move all terms involving \( d \) to one side and constant terms to the other side. Subtract \( 2d \) from both sides:
\[
-3d - 2d + 9 = -1
\]
\[
-5d + 9 = -1
\]

### Step 3: Subtract 9 from both sides to isolate the term with \( d \):
\[
-5d = -1 - 9
\]
\[
-5d = -10
\]

### Step 4: Solve for \( d \) by dividing both sides by -5:
\[
d = \frac{-10}{-5} = 2
\]

### Solution:
\[
d = 2
\]

Do you want further details on the steps or have any questions?

Here are some related problems for practice:
1. Solve: \( 3d + 7 = 5d - 9 \)
2. Solve: \( 4d - 6 + 2d = d + 8 \)
3. Solve: \( 7d - 3d + 5 = 2d + 11 \)
4. Solve: \( 6d + 3 - 4d = 12 \)
5. Solve: \( 8d + 2 = 3d + 15 \)

**Tip:** Always combine like terms first to simplify equations before moving variables to one side.

This detailed guide walks you through solving the linear equation 2d + 9 - 5d = 2d - 1. Learn key algebraic concepts such as combining like terms and solving for a variable, suitable for students in Grades 6-8.

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