- Start with the equation \(20 = -4x\).
- Divide both sides by \(-4\) to isolate the variable \(x\).
- Calculate the result: \(x = \frac{20}{-4} = -5\).
- The solution is \(x = \boxed{-5}\).
Explanation
- Analyzing the equation and isolating x
To solve the linear equation \(20 = -4x\), our goal is to isolate the variable \(x\). We observe that \(x\) is multiplied by \(-4\). To isolate \(x\), we apply the inverse operation of multiplication, which is division. We divide both sides of the equation by \(-4\).
- Calculating the value of x
Dividing both sides of the equation \(20 = -4x\) by \(-4\), we get:
\[\frac{20}{-4} = \frac{-4x}{-4}\]
Simplifying both sides, we find:
\[-5 = x\]
Therefore, the value of \(x\) is \(-5\).
Examples
If a scientist records a temperature decrease of 20 degrees Celsius over a 4-hour period, and the rate of decrease is constant, the equation \(20 = -4x\) (where x is the hourly rate of change) helps determine the hourly change. In this case, \(x = -5\), meaning the temperature drops by 5 degrees Celsius each hour. Such linear equations are fundamental in modeling constant rates of change in physics, economics, and daily life.