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Chapter 3: Problem 26

Simplify the expression. $$-(-6 y+9 x-7)$$

Short Answer

Expert verified
The expression simplifies to \(6y - 9x + 7\).

Step by step solution

01

Distribute the Negative Sign

To simplify the expression \( -(-6y + 9x - 7) \), we need to distribute the negative sign across the terms inside the parentheses. This changes the sign of each term inside. Therefore: \[-6y + 9x - 7\] becomes \[6y - 9x + 7\].
02

Write the Simplified Expression

After distributing the negative sign, the simplified expression is obtained. You simply rewrite it without the parentheses: \[6y - 9x + 7\].

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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 foundation of algebra that helps make complex expressions more manageable. It involves multiplying a single term by each term in a parenthetical expression. In this case, the single term is the negative sign. When you encounter an expression like \(-(-6y + 9x - 7)\), the negative sign has to be distributed across each term in the parentheses.
This means you change the sign of each term:
  • The \(-6y\) becomes \(6y\).
  • The \(9x\) becomes \(-9x\).
  • The \(-7\) becomes \(7\).
Learning how to distribute correctly ensures that you simplify expressions accurately and maintains balance in equations. Mastering this property is essential to advancing in algebra and beyond.
Simplifying Expressions
Simplifying expressions is a crucial skill in algebra that makes equations easier to work with. It involves reducing expressions to their simplest form while maintaining their original value. After utilizing the distributive property in our exercise, the expression \(-(-6y + 9x - 7)\) becomes \([6y - 9x + 7]\).
Once you distribute and change the signs accordingly, the simplified expression should be properly organized:
  • Ensure all like terms are combined.
  • The expression should be free of unnecessary parentheses.
These steps result in a cleaner equation, which can simplify solving further mathematical problems.
Negative Numbers
Working with negative numbers is vital in algebra, as they often appear in various expressions and equations. They have unique properties that are essential to understand for correct mathematical operations.
When distributing a negative sign, such as in \(-(-6y + 9x - 7)\), understanding negative numbers is crucial.
  • Negative times negative results in positive, which explains why \(-(-6y)\) becomes \(6y\).
  • Negative times positive results in negative, seen when \(-9x\) is derived from \(9x\).
Grasping how negative numbers influence other values in equations can reduce errors and increase your confidence in handling complex algebraic expressions.

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Most popular questions from this chapter

Simplify the expression by first using the distributive property to expand the expression, and then rearranging and combining like terms mentally. $$-1-(2 p-8)$$

Solve the equation. $$-6=-5 x+7 x$$

Suppose 2n represents an even whole number. How could we represent the next even number after 2n?

Odd numbers. Evaluate the expression 2n + 1 for the following values: i) n = 1 ii) n = 2 iii) n = 3 iv) n = ?4 v) n = ?5 vi) Is the result always an odd number? Explain.

The width W of a rectangle is 9 feet shorter than its length L. Find the perimeter of the rectangle in terms of its length alone.
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