Verified Answer :

  • Identify the expression \(-2(x+3)\) to be expanded using the distributive property.
  • Multiply \(-2\) by each term inside the parentheses: \(-2 \times x = -2x\) and \(-2 \times 3 = -6\).
  • Combine the terms to get the expanded form \(-2x - 6\).
  • The final simplified expression is \(\boxed{-2x - 6}\).

Explanation

  1. Analyzing and Expanding the Expression

The expression provided is \(-2(x+3)\). To simplify or expand this expression, we apply the distributive property of multiplication over addition, which states that \(a(b + c) = ab + ac\). Here, we distribute the constant \(-2\) across the terms inside the parentheses, \(x\) and \(3\).

  1. Simplifying the Calculation

Applying the distributive property, we have:
\[-2 \times (x + 3) = (-2 \times x) + (-2 \times 3)\]
Calculating these products:
\[-2 \times x = -2x\]
\[-2 \times 3 = -6\]
Combining these results, the expanded form of the expression is \(-2x - 6\). This expression represents a linear function of the form \(f(x) = mx + b\), where the slope \(m\) is \(-2\) and the y-intercept \(b\) is \(-6\).

  1. Final Result

The expanded form of the expression \(-2(x+3)\) is \(-2x - 6\). The variable 'w' in the original prompt is interpreted as a label for the expression. Therefore, the simplified expression is \(\boxed{-2x - 6}\).

Examples

In real-world applications, distributing a negative value can represent calculating a decrease in a quantity over several items. For instance, if you have 3 sets of inventory that are each losing \$2 in value per item @@MATH_TOKEN_23@@, the total change in value can be modeled by @@MATH_TOKEN_24@@. Expanding this to @@MATH_TOKEN_25@@ shows that you lose \$2 for each item \(x\) and an additional fixed loss of \$6.

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