To solve the equation \(6(5x - 3) + 2 = 14\), we'll start by expanding and simplifying it step-by-step:

### Step 1: Distribute the 6
Distribute the \(6\) across the terms inside the parentheses:

\[
6 \cdot (5x) - 6 \cdot 3 + 2 = 14
\]

This simplifies to:

\[
30x - 18 + 2 = 14
\]

### Step 2: Combine like terms
Combine the constant terms \(-18\) and \(+2\):

\[
30x - 16 = 14
\]

### Step 3: Isolate the variable term
Add \(16\) to both sides to isolate the term with \(x\):

\[
30x = 14 + 16
\]

\[
30x = 30
\]

### Step 4: Solve for \(x\)
Divide both sides by \(30\) to solve for \(x\):

\[
x = \frac{30}{30}
\]

\[
x = 1
\]

### Solution
The solution to the equation is:

\[
\boxed{x = 1}
\]

Would you like more details on this, or do you have any other questions?

### Related Questions:
1. How do you solve equations with variables on both sides?
2. What is the process for solving multi-step algebraic equations?
3. How do you handle equations with distribution and combining like terms?
4. What is the importance of isolating the variable when solving equations?
5. How can you check if your solution to an equation is correct?

#### Tip:
Always check your solution by substituting it back into the original equation to verify it satisfies the equation.

Learn how to solve the linear equation 6(5x - 3) + 2 = 14 with a clear, detailed step-by-step solution. This problem introduces key algebraic concepts such as distribution, combining like terms, and isolating variables. Ideal for students in Grades 6-8.

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