To solve the equation \(4(x + 5) + 4x + 8 = 0\), follow these steps:

1. Distribute the 4 in the first term:
   \[
   4(x + 5) = 4x + 20
   \]

2. Substitute this back into the equation:
   \[
   4x + 20 + 4x + 8 = 0
   \]

3. Combine like terms:
   \[
   4x + 4x + 20 + 8 = 0 \implies 8x + 28 = 0
   \]

4. Isolate \(x\) by first subtracting 28 from both sides:
   \[
   8x + 28 - 28 = 0 - 28 \implies 8x = -28
   \]

5. Solve for \(x\) by dividing both sides by 8:
   \[
   x = \frac{-28}{8} \implies x = -\frac{7}{2} \implies x = -3.5
   \]

So, the solution to the equation \(4(x + 5) + 4x + 8 = 0\) is:
\[
x = -3.5
\]

Would you like more details or have any questions?

Here are some related questions to consider:
1. How do you verify that \(x = -3.5\) is the solution to \(4(x + 5) + 4x + 8 = 0\)?
2. How do you solve \(4(x + 5) + 4x + 8 = c\) for a general constant \(c\)?
3. What is the effect of changing the constant term in the equation \(4(x + 5) + 4x + c = 0\)?
4. How do you solve the equation \(4x + 4(x + 5) = 0\) by factoring?
5. What is the graphical representation of \(4(x + 5) + 4x + 8 = 0\)?
6. How do you solve the inequality \(4(x + 5) + 4x + 8 \leq 0\)?
7. How do you solve the equation \(4(x + a) + 4x + b = 0\) for general constants \(a\) and \(b\)?
8. What is the difference between solving \(4(x + 5) + 4x + 8 = 0\) and \(4(x + 5) + 4x + 8 = y\) for \(y \neq 0\)?

**Tip:** When solving linear equations, ensure you isolate the variable on one side to simplify the process.

Learn how to solve the equation 4(x + 5) + 4x + 8 = 0 with a detailed step-by-step solution. This problem covers algebraic concepts, including the distributive property and solving linear equations. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation