Let's solve the equation step by step:

Given equation:
\[
4(-2x + 5) + 5x + 4 = 27
\]

### Step 1: Distribute the \(4\) across the parentheses.
\[
4 \cdot (-2x) + 4 \cdot 5 + 5x + 4 = 27
\]
\[
-8x + 20 + 5x + 4 = 27
\]

### Step 2: Combine like terms.
\[
-8x + 5x + 20 + 4 = 27
\]
\[
-3x + 24 = 27
\]

### Step 3: Subtract 24 from both sides.
\[
-3x = 27 - 24
\]
\[
-3x = 3
\]

### Step 4: Divide by \(-3\) on both sides.
\[
x = \frac{3}{-3}
\]
\[
x = -1
\]

### Solution:
\[
x = -1
\]

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

Here are some related questions for further practice:
1. Solve \(3(2x - 1) + 4 = 10\).
2. Solve \(5x - 3(2x + 1) = 7\).
3. Solve \(7 - 4(x - 2) = 3\).
4. Solve \(2x - (x - 4) + 6 = 10\).
5. Solve \(6(x + 3) + 2 = 20\).

**Tip:** Always distribute and combine like terms carefully to simplify your equations effectively.

Learn how to solve the linear equation 4(-2x + 5) + 5x + 4 = 27 with a detailed step-by-step solution. This problem covers key algebraic concepts such as the distributive property and combining like terms, suitable for students in Grades 7-8.

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