https://file.aiquickdraw.com/mathbot/file/17279901004814yv9wej2.jpg

Let's solve the inequality:

\[
20(x + 1) - 39 < 19x + 1
\]

### Step 1: Distribute the 20 on the left side
\[
20x + 20 - 39 < 19x + 1
\]

Simplify the left side:
\[
20x - 19 < 19x + 1
\]

### Step 2: Move the terms involving \(x\) to one side and constant terms to the other
Subtract \(19x\) from both sides:
\[
20x - 19x - 19 < 1
\]
\[
x - 19 < 1
\]

### Step 3: Isolate \(x\)
Add 19 to both sides:
\[
x < 20
\]

### Solution set:
The solution set is:
\[
x < 20
\]

This means that the solution includes all values of \(x\) less than 20. On a number line, this would be represented as an open circle at \(x = 20\), with the line extending to the left.

Would you like more details on how to graph this on a number line or have any further questions?

### Relative Questions:
1. How do you graph an inequality like \(x < 20\) on a number line?
2. What is the difference between solving equations and inequalities?
3. How would the solution change if the inequality were \(x \leq 20\)?
4. What happens if the inequality sign is flipped (e.g., \(x > 20\))?
5. How do you solve an inequality with fractions?

### Tip:
When solving inequalities, always remember that multiplying or dividing by a negative number flips the inequality sign.

Solve the inequality 20(x + 1) - 39 < 19x + 1.

Learn how to solve the linear inequality 20(x + 1) - 39 < 19x + 1 with a clear, step-by-step solution. This guide covers key algebraic techniques including distribution, combining like terms, and isolating variables, suitable for students in Grades 7-10.

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