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Chapter 10: Problem 10

Simplify. $$ -(4 y-12) $$

Short Answer

Expert verified
The simplified expression is \(-4y + 12\).

Step by step solution

01

Distribute the Negative Sign

The expression given is \(-(4y - 12)\). To simplify, we start by distributing the negative sign across the terms inside the parentheses. This changes the sign of each term inside. The term \(4y\) becomes \(-4y\) and \(-12\) becomes \(+12\).
02

Write the Simplified Expression

Once the distribution is complete, we write the updated version of the expression: \(-4y + 12\). This is the simplified form of the given expression.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Simplifying Expressions
Simplifying expressions is a crucial skill in prealgebra that involves rewriting expressions in their most basic form. The goal is to make the expression as simple as possible while retaining its original value.
In prealgebra, simplifying often involves removing parentheses and combining like terms.
  • First, identify like terms, which are terms that contain the same variable raised to the same power.
  • Combine coefficients of these like terms to simplify.
  • Remove parentheses by distributing or applying other appropriate algebraic rules like expanding or factoring.
Understanding how to simplify expressions helps in solving equations and understanding math concepts. Developing this skill sets a solid foundation for more advanced algebraic operations.
Negative Numbers
Dealing with negative numbers is an important part of simplifying expressions. A negative number is simply a number that's less than zero and can drastically change the outcome of calculations if not handled correctly.
Key points when working with negative numbers include:
  • When you multiply or divide two negative numbers, the result is a positive number.
  • Multiplying or dividing a positive number by a negative number results in a negative number.
  • Addition and subtraction with negative numbers require careful attention to the signs.
In the context of simplifying expressions, being careful with negative numbers ensures that each step of simplification is accurately executed.
Distributive Property
The distributive property is a powerful tool in algebra that allows us to remove parentheses by distributing a factor across terms within those parentheses. It is applied in the form: \[ a(b + c) = ab + ac \]
This property is particularly useful when simplifying expressions like the given exercise, because it lets us break down complex expressions into simpler, manageable parts.
  • First, multiply the factor outside the parentheses by each term inside.
  • Ensure to keep track of positive and negative signs to maintain the expression's accuracy.
  • The distributive property also works in reverse, allowing for factoring out common terms.
Mastering the distributive property aids in solving algebraic equations efficiently and accurately.

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