Verified Answer :

  • The goal is to solve the linear equation \(-10m = 50\) for the variable \(m\).
  • Isolate \(m\) by dividing both sides of the equation by the coefficient \(-10\).
  • Simplify the fraction \(\frac{50}{-10}\) to find the result.
  • The final value is \(\boxed{-5}\).

Explanation

  1. Problem Analysis

The problem asks us to solve the linear equation \(-10m = 50\) for the variable \(m\). A linear equation in one variable expresses a relationship where the variable is multiplied by a constant coefficient. Here, the variable \(m\) is multiplied by -10, resulting in a product of 50. To find the value of \(m\), we need to isolate it on one side of the equation.

  1. Solving for m

To isolate \(m\), we divide both sides of the equation by the coefficient of \(m\), which is -10.
\[ -10m = 50 \]
Dividing both sides by -10:
\[ \frac{-10m}{-10} = \frac{50}{-10} \]
This simplifies to:
\[ m = -5 \]
We can verify this result by substituting -5 back into the original equation: \(-10 \times (-5) = 50\), which is correct.

  1. Final Answer

The value of \(m\) that satisfies the equation \(-10m = 50\) is \(-5\). Thus, the solution is \(\boxed{-5}\).

Examples

Linear equations are used in various real-life situations, such as calculating the number of items you can purchase with a fixed budget. For instance, if a store charges a fee of \(\$10\) per hour for equipment rental, but you have a credit of \(\$50\), you can represent the balance as \(-10h = 50\), where \(h\) is the number of hours you need to work or pay to clear the debt. Understanding how to solve such equations helps in financial planning and resource management.

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