Solve The Equation: ${ -\frac{w}{5} + 9 = 13 }$ { W = \square \}

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 linear equation, ${-\frac{w}{5} + 9 = 13}$, and derive the value of the variable $w$. We will break down the solution into manageable steps, making it easy to understand and follow.

Understanding the Equation

The given equation is ${-\frac{w}{5} + 9 = 13}$. Our goal is to isolate the variable $w$ and find its value. To do this, we need to follow the order of operations (PEMDAS) and perform the necessary algebraic manipulations.

Step 1: Subtract 9 from Both Sides

The first step is to subtract 9 from both sides of the equation. This will help us get rid of the constant term on the left-hand side.

$$-\frac{w}{5} + 9 - 9 = 13 - 9$$

Simplifying the equation, we get:

$$-\frac{w}{5} = 4$$

Step 2: Multiply Both Sides by -5

Next, we need to multiply both sides of the equation by -5 to eliminate the fraction. This will help us isolate the variable $w$.

$$-\frac{w}{5} \times -5 = 4 \times -5$$

Simplifying the equation, we get:

$$w = -20$$

Conclusion

In this article, we solved the linear equation ${-\frac{w}{5} + 9 = 13}$ and derived the value of the variable $w$. By following the order of operations and performing the necessary algebraic manipulations, we were able to isolate the variable $w$ and find its value.

Tips and Tricks

Here are some tips and tricks to help you solve linear equations like this one:

• Always follow the order of operations (PEMDAS).
• Perform the necessary algebraic manipulations to isolate the variable.
• Use inverse operations to eliminate fractions and simplify the equation.
• Check your solution by plugging it back into the original equation.

Real-World Applications

Linear equations have numerous real-world applications in fields such as physics, engineering, and economics. For example, linear equations can be used to model population growth, electrical circuits, and financial transactions.

Common Mistakes

Here are some common mistakes to avoid when solving linear equations:

• Not following the order of operations (PEMDAS).
• Not performing the necessary algebraic manipulations to isolate the variable.
• Not checking the solution by plugging it back into the original equation.

Practice Problems

Here are some practice problems to help you reinforce your understanding of solving linear equations:

• Solve the equation ${2x + 5 = 11}$.
• Solve the equation ${-3x + 2 = 7}$.
• Solve the equation ${x - 4 = 9}$.

Conclusion

Introduction

In our previous article, we discussed how to solve linear equations, focusing on the equation ${-\frac{w}{5} + 9 = 13}$. We broke down the solution into manageable steps and derived the value of the variable $w$. In this article, we will address some common questions and concerns that students may have when solving linear equations.

Q&A

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 know if an equation is linear or not?

A: To determine if an equation is linear, look for the highest power of the variable(s). If the highest power is 1, then the equation is linear. If the highest power is greater than 1, then the equation is not linear.

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

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

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

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

A: To solve a linear equation with fractions, follow these steps:

1. Multiply both sides of the equation by the least common multiple (LCM) of the denominators to eliminate the fractions.
2. Simplify the equation by combining like terms.
3. Isolate the variable by performing inverse operations.

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, whereas a quadratic equation is an equation in which the highest power of the variable(s) is 2. For example, the equation $x + 2 = 5$ is a linear equation, while the equation $x^2 + 4x + 4 = 0$ is a quadratic equation.

Q: How do I check my solution to a linear equation?

A: To check your solution to a linear equation, plug the value of the variable back into the original equation and simplify. If the equation is true, then your solution is correct.

Common Mistakes

Here are some common mistakes to avoid when solving linear equations:

• Not following the order of operations (PEMDAS).
• Not performing the necessary algebraic manipulations to isolate the variable.
• Not checking the solution by plugging it back into the original equation.

Practice Problems

Here are some practice problems to help you reinforce your understanding of solving linear equations:

• Solve the equation ${2x + 5 = 11}$.
• Solve the equation ${-3x + 2 = 7}$.
• Solve the equation ${x - 4 = 9}$.

Conclusion

Solving linear equations is a crucial skill for students to master. By following the order of operations and performing the necessary algebraic manipulations, we can isolate the variable and find its value. Remember to check your solution by plugging it back into the original equation and avoid common mistakes such as not following the order of operations. With practice and patience, you will become proficient in solving linear equations and be able to apply them to real-world problems.