Problem 95 - Beginning and Intermediate Algebra

Question

Write each expression without parentheses. $$ -(-3 q+5 r-8 s) $$

Step-by-Step Solution

Answer

3q - 5r + 8s

Step 1 - Distribute the Negative Sign

To write the expression without parentheses, distribute the negative sign across each term inside the parentheses. Change the signs of each term inside the parentheses.

Step 2 - Change the Sign of Each Term

Change the sign of -3q to 3q +5r to -5r -8s to 8s

Step 3 - Write the New Expression

Combine the terms with their new signs: 3q - 5r + 8s

Key Concepts

Simplifying Expressions

Simplifying expressions in algebra often involves removing parentheses and combining like terms. In our exercise, we started with the expression \(-(-3q + 5r - 8s)\). Our goal was to write this expression without parentheses, which is a common simplification step in algebra.To simplify an expression, you may need to:

• Identify and distribute any coefficients or signs.
• Combine like terms where possible.

By simplifying expressions, you make them easier to work with in equations and other algebraic operations. In this case, the expression was simplified by distributing the negative sign.

Negative Sign Distribution

Negative sign distribution is a key step in the simplification process. In our example, we had to distribute a negative sign across the terms inside the parentheses: \(-(-3q + 5r - 8s)\).When distributing a negative sign, you:

• Change the sign of each term inside the parentheses.

So, \(-(-3q)\) becomes \(3q\), \(-(5r)\) becomes \(-5r\), and \(-(-8s)\) becomes \(8s\). This step transforms the entire expression into new terms:\(3q - 5r + 8s\).Understanding this concept helps you handle more complex algebraic expressions that involve nested operations.

Algebraic Operations

Algebraic operations include addition, subtraction, multiplication, and division of algebraic expressions. In the given exercise, we focused on distribution and sign-changing, which are fundamental operations in algebra.Here are some important points to consider:

• Addition and subtraction: Combine like terms to simplify expressions.
• Distribution: Apply a coefficient or a sign across terms within parentheses.
• Sign-changing: When distributing a negative sign, flip the sign of each term.

In our solution, these operations transformed \(-(-3q + 5r - 8s)\) to \(3q - 5r + 8s\). Mastering these operations will improve your ability to solve and simplify algebraic expressions efficiently.