Simplify to create an equivalent expression.
$2(-14+r)-(-3 r-5)$
Choose 1 answer:
The problem asks us to simplify the algebraic expression \(2(-14 + r) - (-3r - 5)\). This expression involves a variable \(r\) and several constant terms. To simplify, we must perform two main operations: distribution and combining like terms. Our objective is to reduce this to a simple linear form and identify which of the provided options matches our result.
First, we distribute the constant \(2\) across the terms inside the first set of parentheses:
\[2(-14 + r) = 2 \times (-14) + 2 \times r = -28 + 2r.\]
Next, we distribute the negative sign across the second set of parentheses \((-3r - 5)\). Recall that subtracting an expression is equivalent to adding its negation:
\[-(-3r - 5) = -(-3r) - (-5) = 3r + 5.\]
Combining these two parts, the full expression becomes:
\[-28 + 2r + 3r + 5.\]
Now, we combine the like terms. We group the terms involving the variable \(r\) and the constant terms separately:
Putting it all together, we have:
\[5r - 23.\]
Comparing this result with the given choices:
The simplified expression matches option (A).
In many real-world scenarios, such as budgeting or supply chain management, you might work with multiple variables and constants. For example, if a store sells items at a price \(p\) and incurs costs involving both a fixed fee and a variable fee depending on the quantity \(r\), your profit formula might look like an algebraic expression. Simplifying such expressions helps you quickly calculate total profit or loss for different quantities of items sold, ensuring your math is streamlined and your decision-making is efficient.