Given \( h(x)=-x+4 \), solve for \( x \) when \( h(x)=4 \)

To solve the equation \( h(x) = 4 \) for \( x \), we start by substituting \( h(x) \) with its defined expression: \[ -x + 4 = 4 \] Next, we can isolate \( -x \) by subtracting 4 from both sides: \[ -x = 4 - 4 \] This simplifies to: \[ -x = 0 \] To find \( x \), we multiply both sides by -1: \[ x = 0 \] So the solution is \( x = 0 \). Now, let’s look at the broader context! In many real-world scenarios, functions like \( h(x) = -x + 4 \) 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 \( h(x) = 4 \), 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 \( -x \), confusing it with positive values can lead to wrong outcomes. Always double-check operations—especially with negation—before finalizing your answers!