Solve for $b$:
$7b + 2 = 23$
$7b + 2 = 23$
Solve for $b$:
$7b + 2 = 23$
We are given the linear equation \(7b + 2 = 23\) and need to solve for the variable \(b\). A linear equation in one variable is an equation where the highest power of the variable is 1. To isolate the variable \(b\), we will use algebraic manipulation to move the constant terms and then divide by the coefficient of \(b\).
First, we need to move the constant term \(2\) to the right side of the equation. We do this by subtracting \(2\) from both sides:
\[7b + 2 - 2 = 23 - 2\]
\[7b = 21\]
Now that we have the term \(7b\) isolated on one side, we solve for \(b\) by dividing both sides of the equation by the coefficient of \(b\), which is \(7\):
\[\frac{7b}{7} = \frac{21}{7}\]
\[b = 3\]
By following the algebraic steps of isolating the variable \(b\), we have found the solution. The value of \(b\) that satisfies the equation \(7b + 2 = 23\) is \(\boxed{3}\).
Linear equations like this are fundamental in everyday budgeting and resource management. For example, if you have a base fee for a service, such as a streaming subscription or a taxi ride, plus a variable cost per unit (like hourly usage or miles driven), you can use a linear equation to determine exactly how many units you can afford with a fixed total budget. If a taxi company charges a \(\$2\) flat fee plus \(\$7\) per mile, and you have exactly \(\$23\) to spend, solving \(7b + 2 = 23\) helps you calculate that you can travel exactly \(3\) miles.