Write The Letter Above The Solution. 2. Solve For $m$: $\frac{m}{-15} = -4$

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 linear equations, specifically the equation $\frac{m}{-15} = -4$. We will break down the solution step by step, making it easy to understand and follow.

Understanding the Problem

The given equation is $\frac{m}{-15} = -4$. Our goal is to solve for the variable $m$. To do this, we need to isolate $m$ on one side of the equation.

Step 1: Multiply Both Sides by -15

To get rid of the fraction, we can multiply both sides of the equation by -15. This will eliminate the denominator and leave us with a simple linear equation.

\frac{m}{-15} \cdot (-15) = -4 \cdot (-15)

Step 2: Simplify the Equation

After multiplying both sides by -15, we get:

m = 60

Step 3: Check the Solution

To ensure that our solution is correct, we can plug it back into the original equation and check if it satisfies the equation.

\frac{60}{-15} = -4

Since the left-hand side of the equation is equal to the right-hand side, we can confirm that our solution is correct.

Conclusion

Solving linear equations is an essential skill in mathematics, and it requires a step-by-step approach. By following the steps outlined in this article, we can solve equations like $\frac{m}{-15} = -4$ and find the value of the variable $m$. Remember to always check your solution to ensure that it satisfies the original equation.

Tips and Tricks

• When solving linear equations, always start by isolating the variable on one side of the equation.
• Use multiplication and division to eliminate fractions and simplify the equation.
• Check your solution by plugging it back into the original equation.

Common Mistakes to Avoid

• Not checking the solution to ensure that it satisfies the original equation.
• Not following the order of operations when simplifying the equation.
• Not using multiplication and division to eliminate fractions.

Real-World Applications

Solving linear equations has many real-world applications, including:

• Physics: Solving linear equations is essential in physics to describe the motion of objects.
• Engineering: Linear equations are used to design and optimize systems.
• Economics: Solving linear equations is used to model economic systems and make predictions.

Conclusion

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Introduction

In our previous article, we discussed how to solve linear equations, specifically the equation $\frac{m}{-15} = -4$. We broke down the solution step by step, making it easy to understand and follow. In this article, we will answer some common questions related to 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.

Q: How do I solve a linear equation?

To solve a linear equation, you need to isolate the variable on one side of the equation. You can do this by using addition, subtraction, multiplication, and division to get rid of the constants on the other side of the equation.

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 simplifying an equation. 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 handle fractions in linear equations?

When working with fractions in linear equations, you can eliminate them by multiplying both sides of the equation by the denominator. This will get rid of the fraction and leave you with a simple linear equation.

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

A linear equation is an equation in which the highest power of the variable(s) is 1. A quadratic equation, on the other hand, is an equation in which the highest power of the variable(s) is 2. For example, the equation $x^2 + 4x + 4 = 0$ is a quadratic equation, while the equation $2x + 3 = 5$ is a linear equation.

Q: Can I use a calculator to solve linear equations?

Yes, you can use a calculator to solve linear equations. However, it's always a good idea to check your solution by plugging it back into the original equation to make sure it's correct.

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

Some common mistakes to avoid when solving linear equations include:

• Not checking the solution to ensure that it satisfies the original equation.
• Not following the order of operations when simplifying the equation.
• Not using multiplication and division to eliminate fractions.

Q: How do I know if my solution is correct?

To ensure that your solution is correct, you need to plug it back into the original equation and check if it satisfies the equation. If it does, then your solution is correct.

Conclusion

Solving linear equations is a fundamental skill in mathematics, and it requires a step-by-step approach. By following the steps outlined in this article, you can solve linear equations and avoid common mistakes. Remember to always check your solution to ensure that it satisfies the original equation.

Tips and Tricks

• Always start by isolating the variable on one side of the equation.
• Use multiplication and division to eliminate fractions and simplify the equation.
• Check your solution by plugging it back into the original equation.

Real-World Applications

Solving linear equations has many real-world applications, including:

• Physics: Solving linear equations is essential in physics to describe the motion of objects.
• Engineering: Linear equations are used to design and optimize systems.
• Economics: Solving linear equations is used to model economic systems and make predictions.

Conclusion

Solving linear equations is a fundamental skill in mathematics, and it requires a step-by-step approach. By following the steps outlined in this article, you can solve linear equations and avoid common mistakes. Remember to always check your solution to ensure that it satisfies the original equation.