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 [ ].

Solve the equation h x ​ + 1 = − 2 for x in terms of h .
Subtract 1 from both sides: h x ​ = − 3 .
Multiply both sides by h : x = − 3 h .
Substitute h = 4 into x = − 3 h to find x = − 3 ( 4 ) = − 12 . The value of x in terms of h is − 3 h and when h = 4 , x = − 12 . − 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 to solve for a variable in terms of another is crucial in many real-world scenarios. For instance, imagine you're a chef scaling a recipe. If you know the relationship between the amount of flour ( x ) needed and the number of servings ( h ), expressed as x = − 3 h (though in reality, the relationship would be positive), you can easily adjust the recipe. If you need to make it for 4 people, you would calculate x = − 3 ( 4 ) = − 12 . This highlights how algebraic manipulation helps in everyday problem-solving.

Answered by GinnyAnswer | 2025-07-03

The value of x in terms of h is − 3 h , and when h = 4 , x = − 12 .
;

Answered by Anonymous | 2025-07-04