Let's solve the equation step by step:

Given:
\[
-5(2 \cdot x \cdot -2) + 5 \cdot x + 1 = -14
\]

1. Start by simplifying the first term inside the parentheses:
\[
2 \cdot x \cdot -2 = -4x
\]
So, the expression becomes:
\[
-5(-4x) + 5x + 1 = -14
\]

2. Distribute \(-5\) to \(-4x\):
\[
-5(-4x) = 20x
\]
Now the equation is:
\[
20x + 5x + 1 = -14
\]

3. Combine like terms:
\[
(20x + 5x) + 1 = -14
\]
\[
25x + 1 = -14
\]

4. Subtract 1 from both sides:
\[
25x = -14 - 1
\]
\[
25x = -15
\]

5. Finally, divide both sides by 25 to solve for \(x\):
\[
x = \frac{-15}{25} = \frac{-3}{5}
\]

So, \(x = \frac{-3}{5}\).

### Would you like more details or have any questions?

Here are 5 related questions:
1. How do you solve equations with multiple variables?
2. What happens when you distribute a negative sign in an equation?
3. How can you simplify algebraic expressions with parentheses?
4. What are the rules for solving linear equations?
5. What is the process for solving fractions in algebra?

**Tip:** Always simplify inside parentheses first before performing other operations when solving equations.

This guide demonstrates how to solve the linear equation -5(2x - 2) + 5x + 1 = -14 with a detailed, step-by-step explanation. Learn how to simplify algebraic expressions and apply distribution to solve for x. Suitable for students in Grades 8-10.

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