Simplify the following expression:
$4 m-5(-2 m+1)-11$
To simplify the expression \(4m - 5(-2m + 1) - 11\), we start by applying the distributive property to the term \(-5(-2m + 1)\). This means we multiply \(-5\) by each term inside the parentheses. Calculating this gives \(-5 \times (-2m) = 10m\) and \(-5 \times 1 = -5\). Now we substitute this back into our original expression:
\[4m + 10m - 5 - 11\]
Next, we combine the like terms. First, we group the terms with the variable \(m\), which are \(4m\) and \(10m\). Adding these together yields \(4m + 10m = 14m\). Then, we group the constant terms, which are \(-5\) and \(-11\). Adding these constants gives \(-5 - 11 = -16\). Combining these results, the simplified expression is:
\[14m - 16\]
Finally, we compare our simplified expression \(14m - 16\) with the given options:
Our result matches option (D). Therefore, the expression simplifies to \(\boxed{14m - 16}\).
Algebraic simplification is a foundational skill in mathematics used in various real-life scenarios. For example, if you are managing a budget where your income varies as \(4m\) and you have several expenses involving a fixed cost and a variable cost \(5(-2m + 1) + 11\), simplifying the equation helps you quickly calculate your net balance. Mastering these steps ensures that you can handle financial planning, resource allocation, and scientific modeling with precision and ease.