Given , solve for when

To solve the equation for , we start by substituting with its defined expression:

Next, we can isolate by subtracting 4 from both sides:

This simplifies to:

To find , we multiply both sides by -1:

So the solution is .

Now, let’s look at the broader context!

In many real-world scenarios, functions like can represent linear relationships, such as predicting expenses over time where “x” might denote months spent and “h(x)” represents remaining budget. Establishing the point where the function meets a specific value, like , helps in budget management and financial planning.

Making common mistakes is easy when approaching equations! One common error is incorrectly managing the signs. For instance, when isolating , confusing it with positive values can lead to wrong outcomes. Always double-check operations—especially with negation—before finalizing your answers!