Solve for a:
$-16-7 a=5$
$-16-7 a=5$
Solve for a:
$-16-7 a=5$
The problem requires us to solve the linear equation \(-16 - 7a = 5\) for the variable \(a\). This equation is a simple linear relationship where we need to isolate the variable \(a\) on one side to determine its value. Our data consists of the constant \(-16\), the coefficient \(-7\) attached to \(a\), and the result of the expression, which is \(5\).
To solve for \(a\), we first aim to isolate the term containing \(a\). We start by adding \(16\) to both sides of the equation:
\[-16 - 7a + 16 = 5 + 16\]
Simplifying both sides:
\[-7a = 21\]
Now that we have the term \(-7a\) on the left and the constant \(21\) on the right, we solve for \(a\) by dividing both sides by the coefficient \(-7\):
\[a = \frac{21}{-7}\]
Performing the division gives us:
\[a = -3\]
To ensure our solution is correct, we can substitute \(a = -3\) back into the original equation:
\[-16 - 7(-3) = -16 + 21 = 5\]
The equation holds true, so the value of \(a\) is \(-3\). Thus, \(\boxed{-3}\).
Imagine a digital temperature controller that uses a simple linear calibration. If the current display shows \(-16\) and it needs to adjust by a factor of \(-7\) per unit change to reach a target setting of \(5\), you would solve this equation to find how many units of change are required. Understanding linear equations allows you to predict outcomes in scenarios where one quantity is proportional to another, whether in science, finance, or everyday problem solving.