Let's solve the equation step by step.

The given equation is:

\[
19 = 6x + 1 - 3x
\]

### Step 1: Combine like terms on the right side of the equation.

Combine \(6x\) and \(-3x\):

\[
19 = (6x - 3x) + 1
\]

\[
19 = 3x + 1
\]

### Step 2: Isolate the variable term.

Subtract 1 from both sides to isolate the term with \(x\):

\[
19 - 1 = 3x
\]

\[
18 = 3x
\]

### Step 3: Solve for \(x\).

Divide both sides by 3 to solve for \(x\):

\[
x = \frac{18}{3}
\]

\[
x = 6
\]

So, the solution is:

\[
x = 6
\]

Would you like more details or have any questions? Here are some related questions:

1. How do you isolate the variable in an equation?
2. What are like terms, and how do you combine them?
3. How do you solve equations with variables on both sides?
4. What are the steps to check if your solution is correct?
5. What is the difference between solving linear and quadratic equations?

**Tip:** Always combine like terms first to simplify the equation before solving for the variable.

Learn how to solve the equation 19 = 6x + 1 - 3x with a detailed step-by-step solution. This problem involves combining like terms and isolating the variable, suitable for students in Grades 7-9.

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