- Simplify the expression inside the parentheses by combining like terms: \(3x + x = 4x\), resulting in \(-2(4x - 5)\).
- Apply the distributive property: \(-2 \times 4x = -8x\) and \(-2 \times -5 = 10\).
- Combine the results to get the simplified expression: \(-8x + 10\).
- The final simplified expression is \(\boxed{-8x + 10}\).
Explanation
- Combining Like Terms
The given expression to simplify is \(-2(3x + x - 5)\). First, we identify the terms inside the parentheses that can be combined. These are the terms containing the variable \(x\), which are \(3x\) and \(x\). Adding them together, we get \(3x + x = 4x\). Thus, the expression simplifies to \(-2(4x - 5)\).
- Applying the Distributive Property
Next, we apply the distributive property, which states that \(a(b - c) = ab - ac\). In our case, we multiply \(-2\) by each term inside the parentheses:
\(-2 \times (4x) = -8x\)
\(-2 \times (-5) = 10\)
Combining these results, we get \(-8x + 10\).
- Final Result Formulation
Reviewing the original options provided in the question: \(-8x - 10\), \(-8x - 5\), and \(4x - 5\), none of them match the calculated result \(-8x + 10\). Given the steps followed and the application of algebraic rules, the correct simplified form of the expression is \(-8x + 10\).
Examples
The distributive property is a fundamental tool in algebra used to simplify expressions, much like how one might simplify tasks in everyday life. For instance, if you are buying 2 packs of items, and each pack contains 4 pens and you also have to return 5 pens from each pack, you are essentially dealing with the expression \(2(4x - 5)\). Calculating this correctly helps in budgeting or resource management, ensuring that you accurately predict the final count of items in various scenarios.