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Chapter 8: Problem 130

Solve the equation for the variable. $$5 q=44-6 q$$

Short Answer

Expert verified
q = 4

Step by step solution

01

- Combine Like Terms

First, add \( 6q \) to both sides of the equation to combine the \( q \) terms on one side:\[ 5q + 6q = 44 - 6q + 6q \ 11q = 44 \]
02

- Solve for the Variable

Next, divide both sides by \( 11 \) to isolate \( q \):\[ 11q / 11 = 44 / 11 \ q = 4 \]

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Key Concepts

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

Combining Like Terms
When solving linear equations, a key step is combining like terms. Like terms are terms that have the same variable raised to the same power. For example, in the equation \(5q = 44 - 6q\), \(5q\) and \(-6q\) are like terms because they both have the variable \(q\).To combine like terms, move all terms containing the variable to one side of the equation. In this case, add \(6q\) to both sides to get:
  • \(5q + 6q = 44 - 6q + 6q\) which simplifies to:
  • \(11q = 44\).
This process simplifies the equation, making it easier to solve. Always combine like terms first to streamline the solving process!
Isolating Variables
Isolating variables is the next crucial step in solving linear equations. Once we have combined like terms, we want to get the variable by itself on one side of the equation. In our example, after combining like terms, we have \(11q = 44\). To isolate \(q\), we divide both sides of the equation by \(11\). This gives us:
  • \(11q / 11 = 44 / 11\),
  • which simplifies to \(q = 4\).
Isolating the variable helps in finding the solution straightforwardly. Always perform the same operation on both sides of the equation to maintain balance.
Basic Algebra
Basic algebra encompasses the fundamental operations and principles used to solve equations. Understanding these principles is essential in solving problems. Note the following basics observed in our example:
  • Addition and subtraction are used to move terms from one side of the equation to the other.
  • Division and multiplication are used to isolate the variable.
These basic principles are the foundation for more advanced algebra. For example, in \(5q = 44 - 6q\), we used addition to combine like terms and division to isolate the variable. Remembering these basic rules will make solving equations straightforward and intuitive.

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