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To accurately simplify an algebraic expression, it's crucial to understand the order of operations. This is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
This rule helps us determine the sequence in which the operations should be performed to achieve the correct result.

• Parentheses: Solve anything inside parentheses first.
• Exponents: Next, solve exponents.
• Multiplication and Division: These operations come after solving for parentheses and exponents, proceeding from left to right.
• Addition and Subtraction: Finally, addition and subtraction are resolved from left to right.

In the expression \(7 + (x + 10)\), we first assess the content within the parentheses because that's prioritized in PEMDAS.
Only after resolving what's inside the parentheses do we proceed with the remaining operations in the expression.

Parentheses play a significant role in algebra by grouping individual parts of an expression.
They indicate that the enclosed elements must be treated as a single unit and resolved before any other operations in the expression.
In our given expression \(7 + (x + 10)\), the parentheses around \(x + 10\) suggest that these elements should be considered together before any addition outside the parentheses.
This helps clarify which parts of the expression should be handled first, preventing any misunderstanding that could lead to errors in simplification or calculation.
When the expression inside the parentheses is already simplified, as is the case with \(x + 10\), we can then focus on combining it with other parts of the equation outside the parentheses, ensuring accurate results.

Addition in algebraic expressions involves combining terms based on their common factors or nature.
When simplifying, it's vital to add similar terms, often referred to as collecting like terms.
In the expression \(7 + (x + 10)\), once the operations inside parentheses are considered, the next step is addition.
Here, we add the constant 7 to the parenthesized expression. Since \(x\) does not have a like term outside the parentheses, it remains as \(x\).
Therefore, \(7 + 10\) simply combines the constants, totaling 17.
The fully simplified expression, \(x + 17\), reflects how separate components combine while maintaining any variables separate from constants.
This process of addition in algebra is essential for combining terms efficiently and arriving at the simplest form of the expression.