Given $h(x)=-2x+5$, solve for $x$ when $h(x)=3$.
Answer (1)
Substitute h ( x ) = 3 into the equation h ( x ) = − 2 x + 5 .
Subtract 5 from both sides of the equation: − 2 x = − 2 .
Divide both sides by -2: x = 1 .
The solution is 1 .
Explanation
Problem Setup We are given the function h ( x ) = − 2 x + 5 and we want to find the value of x when h ( x ) = 3 . This means we need to solve the equation − 2 x + 5 = 3 for x .
Isolating the x term To solve for x , we first subtract 5 from both sides of the equation: − 2 x + 5 − 5 = 3 − 5 − 2 x = − 2
Solving for x Next, we divide both sides of the equation by -2: − 2 − 2 x = − 2 − 2 x = 1
Final Answer Therefore, when h ( x ) = 3 , the value of x is 1.
Examples
Imagine you are using a machine that produces items at a rate defined by the function h ( x ) = − 2 x + 5 , where x is the time in hours and h ( x ) is the number of items produced. If you want the machine to produce exactly 3 items, you need to determine the time x at which this production level is achieved. By solving the equation − 2 x + 5 = 3 , you find that the machine needs to run for 1 hour to produce 3 items. This kind of problem helps in planning and controlling production processes to meet specific targets.
