Solve for $b$.
$-28-6 b=8$
$-28-6 b=8$
Solve for $b$.
$-28-6 b=8$
We are given the linear equation \(-28 - 6b = 8\). Our goal is to isolate the variable \(b\) to determine its value. This is a standard algebraic equation where we can use the properties of equality—specifically, addition and division—to solve for the unknown.
To isolate the term involving \(b\), we first add \(28\) to both sides of the equation:
\[-28 - 6b + 28 = 8 + 28\]
This simplifies to:
\[-6b = 36\]
Now that we have \(-6b = 36\), we can solve for \(b\) by dividing both sides of the equation by \(-6\):
\[b = \frac{36}{-6}\]
Performing the division, we find:
\[b = -6\]
Imagine you are tracking your bank balance, and it has dropped from a certain amount by an equal weekly deduction over several weeks, eventually reaching a specific balance. If you started with a debt of \(\$28\) and were charged \(\$6\) every week for 6 weeks, your final balance would be \(-28 - (6 \times 6) = -28 - 36 = -64\). Solving for the number of weeks \(b\) in a similar equation helps you manage budgets or determine how long a repeating expense or income stream takes to reach a specific financial target.