Final answer:
In solving an algebraic equation, applying the distributive property is an important step that involves multiplying a term outside the parentheses by each term inside. This leads to elimination of parentheses and simplification of the equation, which aids in finding the variable's value. It is critical to check the answer's reasonableness after solving.
Step-by-step explanation:
The question involves algebra, which is a branch of mathematics concerned with studying the rules of operations and relations and the constructions arising from them. Specifically, this question pertains to using the distributive property to simplify an equation before solving for the variable.
Applying the distributive property means multiplying a single term by each term inside a set of parentheses. This action eliminates the parentheses, making it easier to combine like terms and solve for the unknown variable.
It is a fundamental rule that explains how to combine operations within an expression. It states that when you multiply a number by the sum or difference of two other numbers, you can distribute or "spread out" the multiplication across each term individually. Mathematically, it is expressed as a×(b+c)=a×b+a×c. This property is crucial for simplifying algebraic expressions, factoring, and solving equations. It is applicable in various mathematical contexts, providing a systematic approach to manipulating expressions involving addition, subtraction, and multiplication.