## Simplifying 15 + 6(x + 1): Unveiling the Steps to a Simpler Expression

**Have you ever wondered how to simplify expressions like 15 + 6(x + 1)?** This seemingly complex expression can be broken down into simple, manageable steps using the order of operations. Let's explore the process of simplifying this expression and unlock its hidden simplicity.

**Editor Note:** Simplifying expressions like 15 + 6(x + 1) is a fundamental skill in algebra, crucial for understanding more complex equations and problem-solving.

**Why is this important?** Mastering the art of simplification allows you to effectively manipulate algebraic expressions, making them easier to understand and work with, which is essential for solving equations and understanding mathematical concepts.

**Our analysis:** We will meticulously break down the simplification process of 15 + 6(x + 1), highlighting the key steps involved and explaining the reasoning behind each action. This guide will equip you with the necessary knowledge to confidently simplify similar expressions.

**Key Takeaways of Simplifying Algebraic Expressions:**

Key Takeaway | Explanation |
---|---|

Order of Operations | Follow the order of operations (PEMDAS/BODMAS) for accurate simplification. |

Distributive Property | Apply the distributive property to expand expressions within parentheses. |

Combining Like Terms | Combine terms with the same variable and exponent for a simplified form. |

### Simplifying 15 + 6(x + 1)

**Step 1: Applying the Distributive Property**

The distributive property states that a(b + c) = ab + ac. We apply this to expand the expression 6(x + 1).

```
15 + 6(x + 1) = 15 + 6x + 6
```

**Step 2: Combining Like Terms**

Now, we combine the constant terms, 15 and 6.

```
15 + 6x + 6 = 21 + 6x
```

**Step 3: Final Simplified Expression**

The simplified expression is:

```
21 + 6x
```

This expression cannot be simplified further as the terms are not alike.

### The Power of Simplification

Simplifying expressions is fundamental to solving equations and understanding mathematical concepts. By following the order of operations and applying the distributive property, we can reduce complex expressions to simpler, manageable forms.

### FAQs by Simplifying Algebraic Expressions:

**Q1: What is the order of operations?**
**A1:** The order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), dictates the sequence of operations to solve mathematical expressions.

**Q2: How do I know when an expression is simplified?**
**A2:** An expression is considered simplified when it cannot be further reduced by combining like terms or applying distributive property.

**Q3: Why is the distributive property important?**
**A3:** The distributive property allows us to expand expressions within parentheses, making them easier to manipulate and simplify.

**Q4: Can I simplify 21 + 6x any further?**
**A4:** No, 21 + 6x cannot be simplified further because the terms are not alike (one has an 'x' variable, the other is a constant).

**Q5: How can I practice simplifying algebraic expressions?**
**A5:** Practice is key! Solve various examples and gradually increase the complexity of the expressions to strengthen your understanding.

**Q6: What are some common mistakes to avoid when simplifying expressions?**
**A6:** Common mistakes include forgetting the order of operations, applying the distributive property incorrectly, or failing to combine like terms.

### Tips for Simplifying Algebraic Expressions:

**Always follow PEMDAS:**This will ensure you perform operations in the correct order.**Be mindful of signs:**Pay attention to positive and negative signs when applying the distributive property.**Combine like terms carefully:**Ensure you are adding/subtracting terms with the same variable and exponent.**Check your work:**Verify your simplification steps by substituting values for the variable and comparing the original and simplified expressions.**Practice consistently:**Regular practice will improve your speed and accuracy in simplifying expressions.

### Summary of Simplifying Algebraic Expressions

We have explored the fundamental steps of simplifying algebraic expressions, illustrating the process through the example of 15 + 6(x + 1). By understanding the order of operations, applying the distributive property, and combining like terms, you can efficiently simplify any algebraic expression. This skill is essential for mastering algebra and unlocking the power of mathematical manipulation.

### Closing Message

Simplifying expressions is not just about manipulating symbols but about gaining a deeper understanding of the relationships between numbers and variables. With practice and dedication, you can develop the necessary skills to confidently simplify any algebraic expression, opening doors to a world of mathematical possibilities.