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The distributive property is a key concept in algebra that helps simplify expressions and solve equations. It allows you to multiply a sum by multiplying each addend separately and then adding the products. The distributive property can be expressed as: \( a(b + c) = ab + ac \). In our example, we started with 100[0.06(x+5)]. Using the distributive property, we first distributed 0.06 to both \(x\) and 5 inside the parentheses. This gave us two products: \(0.06x\) and \(0.06 * 5 = 0.30\).

Next, we distributed the 100 to each term in the new expression \(0.06x + 0.30\). We did this by multiplying 100 by each term, resulting in \(100 * 0.06x = 6x\) and \(100 * 0.30 = 30\). So, the original expression simplified to \(6x + 30\).

Using the distributive property can make complex problems simpler and more manageable.

Multiplication is one of the fundamental operations in math and algebra. It is essentially repeated addition. For example, multiplying \(a \times b\) means adding \(a\), \(b\) times. In algebra, multiplication is used to combine numbers and variables.

In the problem we solved, multiplication was used several times:

• First, we multiplied 0.06 by each term inside the parentheses.
• Then, we multiplied the results by 100.

This approach simplifies the expression step by step. In our solution steps, multiplication helped transform \(100[0.06(x+5)]\) into \(6x + 30\). This is because we carefully multiplied each part according to the rules of multiplication.

An algebraic expression is a mathematical phrase that can contain numbers, variables, and operation symbols. These expressions are used to represent real-world problems and simplify complex calculations.

In our example, the expression was 100[0.06(x+5)]. This included:

• Numbers: 100, 0.06, and 5.
• Variable: \(x\).
• Operation symbols: parentheses and multiplication.

The goal was to simplify this expression. By applying the distributive property and multiplication, we turned it into a simpler form, \(6x + 30\).

Understanding how to work with algebraic expressions is crucial for solving equations and simplifying mathematical problems efficiently.