Solve The Equation: − 10 = − 6 + 2 C -10 = -6 + 2c − 10 = − 6 + 2 C

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a simple linear equation, $-10 = -6 + 2c$, using step-by-step instructions and explanations.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

The Equation to be Solved

The equation we will be solving is $-10 = -6 + 2c$. This equation is a simple linear equation, and we will use the steps outlined below to solve for the variable $c$.

Step 1: Isolate the Variable

The first step in solving a linear equation is to isolate the variable. In this case, we need to isolate the variable $c$. To do this, we will add 6 to both sides of the equation.

-10 + 6 = -6 + 6 + 2c
-4 = 2 + 2c

Step 2: Simplify the Equation

The next step is to simplify the equation. In this case, we can simplify the equation by subtracting 2 from both sides.

-4 - 2 = 2 + 2 - 2c
-6 = 0 + 2c

Step 3: Solve for the Variable

The final step is to solve for the variable $c$. To do this, we will divide both sides of the equation by 2.

-6 / 2 = 0 / 2 + 2c / 2
-3 = 0 + c

Conclusion

In this article, we solved the linear equation $-10 = -6 + 2c$ using step-by-step instructions and explanations. We isolated the variable, simplified the equation, and solved for the variable $c$. The final solution is $c = -3$.

Tips and Tricks

• When solving linear equations, it is essential to follow the order of operations (PEMDAS).
• Make sure to isolate the variable before simplifying the equation.
• Use algebraic properties, such as addition and subtraction, to simplify the equation.

Real-World Applications

Linear equations have numerous real-world applications, including:

• Physics: Linear equations are used to describe the motion of objects.
• Engineering: Linear equations are used to design and optimize systems.
• Economics: Linear equations are used to model economic systems.

Common Mistakes

• Failing to isolate the variable before simplifying the equation.
• Not following the order of operations (PEMDAS).
• Not using algebraic properties to simplify the equation.

Conclusion

Solving linear equations is a crucial skill for students to master. By following the steps outlined in this article, students can solve linear equations with ease. Remember to isolate the variable, simplify the equation, and solve for the variable. With practice and patience, students can become proficient in solving linear equations and apply them to real-world problems.

Additional Resources

For additional resources and practice problems, visit the following websites:

• Khan Academy: Linear Equations
• Mathway: Linear Equations
• Wolfram Alpha: Linear Equations

Final Thoughts

Introduction

In our previous article, we discussed how to solve linear equations using step-by-step instructions and explanations. In this article, we will provide a Q&A guide to help students and teachers understand the concepts and techniques involved in solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to follow these steps:

1. Isolate the variable by adding or subtracting the same value to both sides of the equation.
2. Simplify the equation by combining like terms.
3. Solve for the variable by dividing both sides of the equation by the coefficient of the variable.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when evaluating an expression. The acronym PEMDAS stands for:

1. Parentheses: Evaluate 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: How do I isolate the variable?

A: To isolate the variable, you need to add or subtract the same value to both sides of the equation. For example, if you have the equation $x + 3 = 5$, you can isolate the variable by subtracting 3 from both sides:

$x + 3 - 3 = 5 - 3$ $x = 2$

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2. For example:

Linear equation: $x + 2 = 3$ Quadratic equation: $x^2 + 4x + 4 = 0$

Q: Can I use algebraic properties to simplify the equation?

A: Yes, you can use algebraic properties to simplify the equation. For example, if you have the equation $2x + 3 = 5$, you can use the distributive property to simplify the equation:

$2x + 3 = 5$ $2x = 5 - 3$ $2x = 2$ $x = 1$

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

• Failing to isolate the variable before simplifying the equation.
• Not following the order of operations (PEMDAS).
• Not using algebraic properties to simplify the equation.

Q: How can I practice solving linear equations?

A: You can practice solving linear equations by:

• Working through practice problems in a textbook or online resource.
• Using online tools or apps to generate random linear equations.
• Creating your own linear equations and solving them.

Conclusion

Solving linear equations is a crucial skill for students to master. By following the steps outlined in this article and practicing regularly, students can become proficient in solving linear equations and apply them to real-world problems. Remember to isolate the variable, simplify the equation, and solve for the variable. With practice and patience, students can become experts in solving linear equations.

Additional Resources

For additional resources and practice problems, visit the following websites:

• Khan Academy: Linear Equations
• Mathway: Linear Equations
• Wolfram Alpha: Linear Equations

Final Thoughts

Solving linear equations is a fundamental concept in mathematics, and it has numerous real-world applications. By mastering the skills outlined in this article, students can become proficient in solving linear equations and apply them to real-world problems. Remember to practice regularly and seek help when needed. With dedication and hard work, students can become experts in solving linear equations.