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The distributive property is a basic principle you'll frequently use in prealgebra. It allows you to multiply a single term by terms inside parentheses. This property is like handing out a task to each member of a group, ensuring everyone gets their fair share. To apply this property effectively, you multiply the term outside the parentheses by each term within.
For instance, with the example expression \(-3(n-1)\), you apply the distributive property by multiplying -3 by \(n\) and \(-1\). This results in two separate products: \(-3 imes n = -3n\) and \(-3 imes (-1) = 3\). Thus, you obtain \(-3n + 3\).

By using the distributive property, you break down a complex expression into simpler parts, making it easier to manage and solve.

Once you've applied the distributive property, the next step in simplifying an expression is to combine like terms. "Like terms" are those that contain the same variables raised to the same power. This means they have identical variable factors, allowing them to be combined by adding or subtracting their coefficients.
For the given expression \(-3n + 3 - 4n\), notice that \(-3n\) and \(-4n\) are like terms because they both contain the variable \(n\).
To combine these, you simply add their coefficients:

• -3 + -4 = -7

The new combined term is \(-7n\).

Combining like terms streamlines expressions, reducing the number of terms and simplifying the overall problem. It’s a vital skill in prealgebra that sets the foundation for solving more complex equations.

Prealgebra is the bridge between basic arithmetic and the more advanced world of algebra. It involves understanding fundamental concepts that are pivotal in solving equations, like using the distributive property and combining like terms. These basics not only simplify expressions but also prepare you for more challenging math problems you will encounter in the future.
Key skills in prealgebra include:

• Understanding how to manipulate expressions and equations
• Learning effective techniques for simplifying problems
• Developing problem-solving strategies to tackle various types of math challenges

Being proficient in these basics will give you a robust foundation for progressing in your mathematical journey. Embrace these concepts with practice and patience, as they are crucial stepping stones in building mathematical fluency.