Solve For \[$ C \$\].$\[ \begin{array}{c} -3(c-5)=-3 \\ c=[?] \end{array} \\]

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Introduction

In this article, we will delve into the world of algebra and solve for the variable c in the given equation. We will break down the problem into manageable steps, making it easy to understand and follow along.

The Equation

The given equation is:

−3(c−5)=−3-3(c-5)=-3

Our goal is to isolate the variable c and find its value.

Step 1: Distribute the Negative 3

To start solving the equation, we need to distribute the negative 3 to the terms inside the parentheses.

−3(c−5)=−3-3(c-5)=-3

−3c+15=−3-3c+15=-3

Step 2: Add 3 to Both Sides

Next, we need to get rid of the negative term on the left side of the equation. We can do this by adding 3 to both sides of the equation.

−3c+15=−3-3c+15=-3

−3c+15+3=−3+3-3c+15+3=-3+3

−3c+18=0-3c+18=0

Step 3: Subtract 18 from Both Sides

Now, we need to isolate the term with the variable c. We can do this by subtracting 18 from both sides of the equation.

−3c+18=0-3c+18=0

−3c+18−18=0−18-3c+18-18=0-18

−3c=−18-3c=-18

Step 4: Divide Both Sides by -3

Finally, we need to get rid of the coefficient -3 that is being multiplied by the variable c. We can do this by dividing both sides of the equation by -3.

−3c=−18-3c=-18

−3c−3=−18−3\frac{-3c}{-3}=\frac{-18}{-3}

c=6c=6

Conclusion

And there you have it! We have successfully solved for the variable c in the given equation. By following the steps outlined above, we were able to isolate the variable c and find its value.

Tips and Tricks

  • When solving equations, it's essential to follow the order of operations (PEMDAS) to ensure that you are performing the operations in the correct order.
  • When distributing a negative term, make sure to change the sign of each term inside the parentheses.
  • When adding or subtracting a term to both sides of an equation, make sure to change the sign of the term on the other side of the equation.

Real-World Applications

Solving for variables is a crucial skill in many real-world applications, including:

  • Physics: Solving for variables is essential in physics to describe the motion of objects and predict their behavior.
  • Engineering: Solving for variables is critical in engineering to design and optimize systems, such as bridges and buildings.
  • Economics: Solving for variables is essential in economics to model and analyze economic systems and make informed decisions.

Final Thoughts

Introduction

In our previous article, we delved into the world of algebra and solved for the variable c in the given equation. In this article, we will answer some of the most frequently asked questions about solving for variables.

Q: What is the first step in solving for a variable?

A: The first step in solving for a variable is to isolate the variable on one side of the equation. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: How do I know which operation to perform first?

A: To determine which operation to perform first, you need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate any expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the difference between a coefficient and a variable?

A: A coefficient is a number that is multiplied by a variable, while a variable is a letter or symbol that represents a value that can change.

Q: How do I distribute a negative term?

A: When distributing a negative term, you need to change the sign of each term inside the parentheses. For example, if you have the expression:

−3(x+2)-3(x+2)

You would distribute the negative 3 as follows:

−3x−6-3x-6

Q: What is the purpose of adding or subtracting a term to both sides of an equation?

A: Adding or subtracting a term to both sides of an equation is used to isolate the variable on one side of the equation. This is done by making the coefficient of the variable equal to 1.

Q: How do I know if I have solved for the variable correctly?

A: To check if you have solved for the variable correctly, you can plug the value of the variable back into the original equation and see if it is true.

Q: What are some common mistakes to avoid when solving for variables?

A: Some common mistakes to avoid when solving for variables include:

  • Not following the order of operations (PEMDAS)
  • Not distributing negative terms correctly
  • Not adding or subtracting terms to both sides of the equation correctly
  • Not checking the solution by plugging the value of the variable back into the original equation

Q: How do I apply solving for variables to real-world problems?

A: Solving for variables is a crucial skill in many real-world applications, including:

  • Physics: Solving for variables is essential in physics to describe the motion of objects and predict their behavior.
  • Engineering: Solving for variables is critical in engineering to design and optimize systems, such as bridges and buildings.
  • Economics: Solving for variables is essential in economics to model and analyze economic systems and make informed decisions.

Q: What are some resources for learning more about solving for variables?

A: Some resources for learning more about solving for variables include:

  • Online tutorials and videos
  • Algebra textbooks and workbooks
  • Online communities and forums
  • Math apps and software

Conclusion

Solving for variables is a fundamental concept in algebra that has numerous real-world applications. By following the steps outlined above and avoiding common mistakes, you can successfully solve for variables and apply this skill to a wide range of problems. Remember to always follow the order of operations (PEMDAS), distribute negative terms correctly, and add or subtract terms to both sides of an equation with caution.