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When we say 'simplifying expressions', we mean making them more compact or easier to handle. In algebra, this often involves combining like terms or reducing the number of terms as much as possible.

In our given exercise, \(-(r+7)\), simplifying it using the distributive property can make it clearer. We applied the distributive property by multiplying each term inside the parentheses by the negative sign outside.

This helps in reducing the given expression to its simplest form, by expressing it as \(-r - 7\). It's a key step in algebra that allows for easier manipulation and understanding of equations and expressions. Regular practice simplifies handling more complex expressions in the future!

Negative numbers can sometimes be tricky, but understanding how they work is critical in algebra.

In the exercise, we had to distribute a negative sign \(-1\) across the terms in the expression \(-(r+7)\). Here's what happens:

• \-1 multiplied by \(r\) becomes \-r\
• \-1 multiplied by \7\ becomes \-7\

The result is the expression \-r - 7\.
It's essential to remember that when you multiply a negative number by a positive number, the result is always negative.

This fundamental property of negative numbers helps in simplifying expressions and solving equations accurately.

Understanding algebraic properties is essential for working comfortably with expressions and equations. These properties, such as the distributive property, help us manipulate and simplify expressions.

In the context of our exercise, we used the distributive property, defined as \[a(b + c) = ab + ac\]. This property lets us distribute a single term across terms inside parentheses.
For our expression, \(-(r+7)\), we applied it as follows:

• Multiply \-1\ by \(r\) to get \-r\
• Multiply \-1\ by \7\ to get \-7\

Using algebraic properties like this makes our work easier and ensures we maintain accuracy throughout our calculations.
Mastering these properties lays a solid foundation in algebra and boosts your problem-solving skills in mathematics.