Let's solve the equation step by step:

Given equation:
\[
14x + 1 = 10x - 19
\]

1. Subtract \(10x\) from both sides to get the \(x\) terms on one side:
\[
14x - 10x + 1 = -19
\]
\[
4x + 1 = -19
\]

2. Subtract 1 from both sides to isolate the term with \(x\):
\[
4x = -19 - 1
\]
\[
4x = -20
\]

3. Divide both sides by 4 to solve for \(x\):
\[
x = \frac{-20}{4}
\]
\[
x = -5
\]

So, the solution is:
\[
\boxed{x = -5}
\]

Would you like more details or have any questions?

Here are five related questions you might find useful:

1. How would you solve the equation \(7x + 3 = 5x - 11\)?
2. What happens if both sides of the equation have the same term, e.g., \(12x + 4 = 12x - 8\)?
3. How do you solve the equation \(9y + 6 = 2(4y - 7)\)?
4. What is the value of \(x\) if \(8x - 15 = 3x + 10\)?
5. How do you isolate \(x\) in the equation \(6x + 9 = 3x + 12\)?

**Tip:** When solving linear equations, always aim to isolate the variable on one side of the equation by using inverse operations (addition, subtraction, multiplication, or division).

Learn how to solve the equation 14x + 1 = 10x - 19 step-by-step with a detailed solution. This problem involves solving linear equations using inverse operations. Suitable for students in Grades 7-9.

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