Solve For { N $} . . . { 2(n+5) = -2 \}

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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 specific type of linear equation, namely the equation 2(n+5) = -2. We will break down the solution step by step, using clear and concise language to ensure that readers understand the process.

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. Linear equations can be solved using various methods, including algebraic manipulation and graphical methods.

The Equation 2(n+5) = -2

The equation 2(n+5) = -2 is a linear equation in which the variable n is multiplied by 2 and then added to 10 (since 2*5 = 10). The equation can be rewritten as 2n + 10 = -2.

Step 1: Isolate the Variable

To solve the equation, we need to isolate the variable n. We can do this by subtracting 10 from both sides of the equation. This will give us 2n = -2 - 10.

# Subtract 10 from both sides of the equation
equation = "2n + 10 = -2"
new_equation = "2n = -2 - 10"
print(new_equation)

Step 2: Simplify the Equation

The right-hand side of the equation can be simplified by combining the constants. -2 - 10 = -12.

# Simplify the right-hand side of the equation
new_equation = "2n = -12"
print(new_equation)

Step 3: Divide Both Sides by 2

To isolate the variable n, we need to divide both sides of the equation by 2. This will give us n = -12/2.

# Divide both sides of the equation by 2
new_equation = "n = -12/2"
print(new_equation)

Step 4: Simplify the Right-Hand Side

The right-hand side of the equation can be simplified by dividing -12 by 2. -12/2 = -6.

# Simplify the right-hand side of the equation
new_equation = "n = -6"
print(new_equation)

Conclusion

In this article, we have solved the linear equation 2(n+5) = -2 using a step-by-step approach. We have isolated the variable n, simplified the equation, and finally solved for n. The solution is n = -6.

Tips and Tricks

  • When solving linear equations, it is essential to follow the order of operations (PEMDAS).
  • Use algebraic manipulation to simplify the equation and isolate the variable.
  • Check your solution by plugging it back into the original equation.

Real-World Applications

Linear equations have numerous real-world applications, including:

  • Physics: equations are used to describe the motion of objects under constant acceleration.
  • Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
  • Economics: Linear equations are used to model economic systems and make predictions about future trends.

Conclusion

Introduction

In our previous article, we solved the linear equation 2(n+5) = -2 using a step-by-step approach. In this article, we will answer some frequently asked questions about solving linear equations.

Q: 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.

Q: How do I solve a linear equation?

To solve a linear equation, you need to isolate the variable. You can do this by using algebraic manipulation, such as adding or subtracting the same value to both sides of the equation, or multiplying or dividing both sides of the equation by the same non-zero value.

Q: What is the order of operations?

The order of operations is a set of rules that tells you which operations to perform first when you have multiple operations in an expression. The order of operations is:

  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 simplify an equation?

To simplify an equation, you need to combine like terms. Like terms are terms that have the same variable raised to the same power. You can combine like terms by adding or subtracting their coefficients.

Q: What is a coefficient?

A coefficient is a number that is multiplied by a variable. For example, in the equation 2x + 3, the coefficient of x is 2.

Q: How do I check my solution?

To check your solution, you need to plug it back into the original equation and see if it is true. If it is true, then your solution is correct.

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

Some common mistakes to avoid when solving linear equations include:

  • Not following the order of operations
  • Not combining like terms
  • Not checking your solution
  • Not using algebraic manipulation to isolate the variable

Q: How do I solve a linear equation with fractions?

To solve a linear equation with fractions, you need to eliminate the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators.

Q: How do I solve a linear equation with decimals?

To solve a linear equation with decimals, you need to eliminate the decimals by multiplying both sides of the equation by a power of 10.

Conclusion

Solving linear equations is a crucial skill for students to master. By following a step-by-step approach and using algebraic manipulation, we can solve even the most complex linear equations. In this article, we have answered some frequently asked questions about solving linear equations. We hope that this article has provided readers with a deeper understanding of linear and their applications.

Tips and Tricks

  • Always follow the order of operations when solving linear equations.
  • Use algebraic manipulation to simplify the equation and isolate the variable.
  • Check your solution by plugging it back into the original equation.
  • Use the least common multiple (LCM) to eliminate fractions.
  • Use a power of 10 to eliminate decimals.

Real-World Applications

Linear equations have numerous real-world applications, including:

  • Physics: equations are used to describe the motion of objects under constant acceleration.
  • Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
  • Economics: Linear equations are used to model economic systems and make predictions about future trends.

Conclusion

Solving linear equations is a crucial skill for students to master. By following a step-by-step approach and using algebraic manipulation, we can solve even the most complex linear equations. In this article, we have answered some frequently asked questions about solving linear equations. We hope that this article has provided readers with a deeper understanding of linear equations and their applications.