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Chapter 2: Problem 41

Solve \(-F-G=300\) for \(G\)

Short Answer

Expert verified
G = -(300 + F)

Step by step solution

01

Isolate the variable term

Start by isolating the term with the variable on one side of the equation. Add \( F \) to both sides of the equation to get: \(-G = 300 + F \).
02

Solve for the variable

To solve for \( G \), multiply both sides of the equation by \( -1 \) to reverse the sign: \( G = - (300 + F) \).

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Key Concepts

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

Isolate Variable
In algebra, one of the first steps to solving an equation is to isolate the variable you're solving for. This means rearranging the equation so that the variable is by itself on one side of the equation. For instance, in the exercise (-F-G=300), we aim to isolate G.
First, add F to both sides of the equation. This step doesn't change the value of the equation because what you do to one side, you must do to the other. So, (-F-G + F = 300 + F) simplifies to (-G = 300 + F). Now, G is isolated with a negative sign.
Always remember: to isolate a variable:
  • Perform the same operation on both sides of the equation
  • Use addition or subtraction first to get the variable term by itself
  • Keep the equation balanced
Reverse Sign
Often, after isolating the variable, we may need to get rid of a negative sign. This is called reversing the sign. In our example, after isolating G, we have (-G = 300 + F), but G is negative. To make G positive, multiply both sides of the equation by (-1). That operation flips the signs on both sides: G = - (300 + F).
Reversing the sign is essential to make sure the variable is positive, which is standard practice. Here are some quick reminders:
  • Multiplying by -1 will change the sign of each term
  • The goal is to make the variable positive if it was isolated with a negative sign
  • Keep the balance by performing the same operation on both sides
Linear Equations
Linear equations are equations where the variable is raised only to the first power. They are called linear because their graph forms a straight line. The general form of a linear equation is (ax + b = c). In our sample problem, even though there are no x's, (-F-G=300) is still linear.
Linear equations are simple and foundational. To solve one:
  • Identify the variable and constants
  • Apply inverse operations to isolate the variable
  • Simplify, ensuring each step keeps the equation balanced
Solving linear equations efficiently requires understanding these basic operations. Once mastered, they provide the foundation for more complex algebraic equations.

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