Let's simplify the given expression step by step.

The expression is:

\[
\frac{5(2x - 6)}{10} - 2
\]

### Step 1: Simplify the numerator.
Expand \( 5(2x - 6) \):

\[
5(2x - 6) = 10x - 30
\]

Now the expression becomes:

\[
\frac{10x - 30}{10} - 2
\]

### Step 2: Simplify the fraction.
Divide each term in the numerator by 10:

\[
\frac{10x}{10} - \frac{30}{10} = x - 3
\]

Now the expression is:

\[
x - 3 - 2
\]

### Step 3: Simplify the constants.
Combine \(-3\) and \(-2\):

\[
x - 3 - 2 = x - 5
\]

Thus, the simplified expression is:

\[
x - 5
\]

Would you like more details on any of the steps?

Here are 5 related questions you might find useful:
1. How do you expand expressions with parentheses?
2. How do you distribute terms in algebra?
3. What is the process of simplifying fractions in algebraic expressions?
4. How do you combine like terms in an expression?
5. What are the rules for solving algebraic expressions with variables?

**Tip:** Always expand parentheses first before simplifying terms in an expression.

Explore how to simplify the algebraic expression [5(2x - 6)]/10 - 2 with step-by-step explanations. This problem involves expanding parentheses, using the distributive property, and combining like terms, making it ideal for students in Grades 6-8.

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