Type the correct answer in each box. Use numerals instead of words.
Consider the equation below.
[tex]\frac{x}{h}+1=-2[/tex]
The value of [tex]x[/tex] in terms of [tex]h[/tex] is [ ].
The value of [tex]x[/tex] when [tex]h=4[/tex] is [ ]
Answer (1)
First, isolate h x by subtracting 1 from both sides: h x = − 3 .
Then, solve for x in terms of h by multiplying both sides by h : x = − 3 h .
Substitute h = 4 into the equation x = − 3 h .
Calculate the value of x : − 12 .
Explanation
Problem Analysis We are given the equation h x + 1 = − 2 Our goal is to find the value of x in terms of h , and then find the value of x when h = 4 .
Isolating x/h First, let's solve for x in terms of h . To isolate x , we first subtract 1 from both sides of the equation: h x + 1 − 1 = − 2 − 1 h x = − 3
Solving for x in terms of h Next, we multiply both sides of the equation by h to solve for x :
h x × h = − 3 × h x = − 3 h
Finding x when h=4 Now that we have x in terms of h , we can find the value of x when h = 4 . We substitute h = 4 into the equation x = − 3 h :
x = − 3 ( 4 ) x = − 12
Final Answer Therefore, the value of x in terms of h is − 3 h , and the value of x when h = 4 is − 12 .
Examples
Understanding how variables relate and change with respect to each other is crucial in many real-world applications. For instance, in physics, the distance an object travels ( x ) can be related to its speed ( − 3 ) and the time it travels ( h ) by the formula x = − 3 h . If you know the time an object travels, you can easily calculate the distance it covers. Similarly, in economics, the profit of a company ( x ) can be related to the number of products sold ( h ) with a certain profit margin ( − 3 ). By understanding these relationships, you can make informed decisions and predictions.
