Solve for b:
$\frac{b}{-12}=-6$
The objective is to solve the linear equation \(\frac{b}{-12} = -6\) for the variable \(b\). This equation involves a single variable \(b\) being divided by a constant, \(-12\), and equated to another constant, \(-6\). The goal is to isolate \(b\) on one side of the equation to determine its value.
To isolate the variable \(b\), we need to perform the inverse operation of division. Since \(b\) is currently divided by \(-12\), we multiply both sides of the equation by \(-12\). This will cancel out the denominator on the left side, leaving \(b\) by itself. The operation is as follows:
\[\frac{b}{-12} \times (-12) = -6 \times (-12)\]
Now, we perform the multiplication on both sides:
On the left side, \(\frac{b}{-12} \times (-12) = b\).
On the right side, \(-6 \times (-12) = 72\).
Therefore, \(b = 72\). This is the value that satisfies the given equation. We can verify this by plugging the value back into the original equation: \(\frac{72}{-12} = -6\), which is correct.
In real-life, equations like this are common when dealing with averages or scaled measurements. For example, if you know that a temperature dropped by an average of 6 degrees per hour for 12 hours, you can find the total temperature change, \(b\), by setting up \(\frac{b}{12} = -6\), or in this case, representing the negative drop with \(\frac{b}{-12} = -6\). Solving for \(b\) tells you the total change in temperature, which would be \(-72\) degrees. Understanding these simple linear relationships helps in predicting outcomes based on constant rates of change.