Let's solve the equation step by step:

### Given:
\[
2k - 3(2k - 3) = 45
\]

### Step 1: Expand the expression
Distribute \(-3\) across \((2k - 3)\):
\[
2k - 3(2k) + 3(3) = 45
\]
\[
2k - 6k + 9 = 45
\]

### Step 2: Combine like terms
\[
(2k - 6k) + 9 = 45
\]
\[
-4k + 9 = 45
\]

### Step 3: Isolate the variable term
Subtract 9 from both sides:
\[
-4k = 45 - 9
\]
\[
-4k = 36
\]

### Step 4: Solve for \(k\)
Divide both sides by \(-4\):
\[
k = \frac{36}{-4}
\]
\[
k = -9
\]

### Final Solution:
\[
k = -9
\]

Would you like further explanation or have any questions? Here are some related questions to explore:

1. What is the general method for solving linear equations?
2. How do you distribute a number across parentheses in algebra?
3. How do you combine like terms?
4. What is the importance of isolating the variable?
5. How would the equation change if the constant on the right was different?

**Tip:** Always double-check your distribution when solving algebraic equations to avoid small errors.

Learn how to solve the linear equation 2k - 3(2k - 3) = 45 with a detailed step-by-step explanation. This algebra problem focuses on the distributive property, combining like terms, and isolating the variable. Suitable for students in Grades 6-8.

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