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Chapter 7: Problem 76

Write an equivalent expression without parentheses. $$-(3-a)$$

Short Answer

Expert verified
-3 + a

Step by step solution

01

Understand the Problem

Given the expression \(- (3 - a)\), the goal is to remove the parentheses and simplify the expression.
02

Distribute the Negative Sign

Apply the negative sign to each term inside the parentheses. Remember that distributing a negative sign changes the sign of each term inside the parentheses.
03

Simplify Each Term

Distributing the negative sign, we get: \(- (3 - a) = -3 + a\).
04

Write the Final Expression

Combine the terms to write the equivalent expression without parentheses: \(-3 + a\).

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Key Concepts

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

distributive property
The distributive property is a fundamental concept in algebra. It allows you to multiply a single term by each term within parentheses. This process helps simplify expressions and solve equations effectively.
For example: When you have an expression like \(a(b + c)\), you can apply the distributive property to get \(ab + ac\).
This property is especially useful when dealing with parentheses. Instead of solving what's inside first, you can distribute the term outside the parentheses right away.
negative sign distribution
The negative sign distribution follows similar rules to distributing any other number. When you distribute a negative sign across a term inside parentheses, you change the sign of each term within the parentheses.
For example: Consider the expression \(-(3 - a)\). Distributing the negative sign, you'd get \(-3 + a\).
This step is crucial in algebra as it ensures that all terms are treated equally and correctly simplified.
expression simplification
Expression simplification involves reducing an algebraic expression to its simplest form. This means removing parentheses, combining like terms, and making the expression as straightforward as possible.
For instance: Following our example \(-(3 - a)\), you distribute the negative sign to get \(-3 + a\). Here, there are no like terms to combine, so this is the simplified form.
Simplifying expressions makes it easier to understand and solve algebraic equations. It's a critical step in the problem-solving process.

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Most popular questions from this chapter

Is the following statement true or false: "For any real numbers \(a, b,\) and \(c,\) if \(a c=b c,\) then \(a=b^" ?\) Explain why you answered as you did.

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Solve. $$\frac{\frac{1}{3}}{x}=\frac{1-\frac{1}{x}}{x}$$

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