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Chapter 2: Problem 42

Solve \(-H-K=800\) for \(K\)

Short Answer

Expert verified
K = -800 - H

Step by step solution

01

- Isolate the term with K

Rewrite the equation -H-K=800 to isolate the term with K. To do this, add H to both sides of the equation: -K = 800 + H.
02

- Solve for K

Divide both sides of the equation by -1 to solve for K: K = -(800 + H). This simplifies to K = -800 - H.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

algebraic manipulation
Algebraic manipulation refers to the techniques used to simplify or rearrange equations. These techniques are essential in solving equations and understanding relationships between variables.
In our example, the goal is to isolate the variable K. To start, we need to manipulate the original equation \( -H - K = 800 \).
The first step is to move the terms around to bring the variable of interest into focus. To do this:
  • Add H to both sides of the equation. This step helps in getting rid of the H-term on the left side:
    • \[-H - K + H = 800 + H\]
  • Once simplified, it becomes:
    • \-K = 800 + H\.
    This step-by-step rearrangement involves basic addition and subtraction, essential methods in algebra. Mastering these techniques makes solving complex equations easier.
isolating variables
Isolating a variable means getting the variable alone on one side of the equation. This is a crucial part of solving equations as it allows us to clearly see the value of the variable we're focusing on.
In our example, after simplifying to \( -K = 800 + H \), the next logical step is to isolate K.
To isolate K, we need to deal with the negative sign in front of K. This can be done by performing the opposite operation, which in this case is dividing by -1. By doing so, we isolate K:
  • Divide both sides of the equation by -1:
    • \-K / -1 = (800 + H) / -1\
    When simplified, it becomes: \K = -800 - H\
    Now, K is isolated, and its relationship with H is clear.
    Understanding how to isolate variables is fundamental in algebra. It allows students to transform complex equations into simpler, more manageable ones.
solving for a variable
Solving for a variable involves finding the value of the variable that makes the equation true. This process requires a clear understanding of algebraic manipulation and isolating variables.
In our case, after isolating K, we've arrived at the equation \( K = -800 - H \).
To solve for K, you:
  • First identified the term with K in the original equation.
  • Then manipulated the equation to move other terms to the opposite side.
  • And finally, isolated K by reversing operations like multiplication or division.
By these steps, we've found that the value of K depends on the value of H.
This means for any given H, we can determine K.
Solving for a variable helps break down complex equations into understandable parts, leading to more accurate mathematical solutions and deeper comprehension of algebraic relationships.

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