Given [tex]h(x)=-x+5[/tex], solve for [tex]x[/tex] when [tex]h(x)=0[/tex].
Answer (1)
Set the function h ( x ) equal to 0: − x + 5 = 0 .
Add x to both sides of the equation: 5 = x .
The solution is x = 5 .
Therefore, the value of x when h ( x ) = 0 is 5 .
Explanation
Problem Analysis We are given the function h ( x ) = − x + 5 and we want to find the value of x such that h ( x ) = 0 . This means we need to solve the equation − x + 5 = 0 for x .
Solving for x To solve the equation − x + 5 = 0 , we want to isolate x on one side of the equation. We can do this by adding x to both sides of the equation: − x + 5 + x = 0 + x
5 = x
Final Answer Therefore, the value of x that satisfies h ( x ) = 0 is x = 5 .
Examples
Imagine you're on a diet and want to know how many days it will take to reach your goal weight. If your weight loss can be modeled by the function h ( x ) = − x + 5 , where h ( x ) is your weight loss after x days, setting h ( x ) = 0 helps you determine when you'll reach your goal weight. In this case, it will take 5 days to reach your goal.
