Show All Calculations. Calculate The Following:${ \begin{array}{l} -64 \ -4x - 7 \end{array} }$

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 with one variable, specifically the equation $-4x - 7$. We will also explore how to show all calculations, which is an essential aspect of problem-solving in mathematics.

Understanding the Equation

The given equation is $-4x - 7$. To solve for $x$, we need to isolate the variable $x$ on one side of the equation. The equation is already in a simple form, but we can simplify it further by adding $7$ to both sides of the equation.

Adding 7 to Both Sides

When we add $7$ to both sides of the equation, we get:

$$-4x - 7 + 7 = -4x$$

This simplifies to:

$$-4x = -4x + 7 - 7$$

Simplifying the Equation

Now, we can simplify the equation further by combining like terms:

$$-4x = -7$$

Dividing Both Sides by -4

To solve for $x$, we need to divide both sides of the equation by $-4$. This will give us:

$$\frac{-4x}{-4} = \frac{-7}{-4}$$

This simplifies to:

$$x = \frac{7}{4}$$

Showing All Calculations

To show all calculations, we can rewrite the equation as follows:

$$-4x - 7 + 7 = -4x$$

$$-4x = -7$$

$$\frac{-4x}{-4} = \frac{-7}{-4}$$

$$x = \frac{7}{4}$$

By showing all calculations, we can ensure that our solution is accurate and that we have followed the correct steps to solve the equation.

Conclusion

Solving linear equations is an essential skill in mathematics, and showing all calculations is a crucial aspect of problem-solving. By following the steps outlined in this article, we can solve linear equations with one variable and ensure that our solutions are accurate.

Real-World Applications

Linear equations have many real-world applications, including:

• Finance: Linear equations can be used to calculate interest rates, investment returns, and other financial metrics.
• Science: Linear equations can be used to model population growth, chemical reactions, and other scientific phenomena.
• Engineering: Linear equations can be used to design and optimize systems, including electrical circuits, mechanical systems, and other engineering applications.

Tips and Tricks

Here are some tips and tricks for solving linear equations:

• Use inverse operations: To solve for $x$, use inverse operations to isolate the variable on one side of the equation.
• Combine like terms: Combine like terms to simplify the equation and make it easier to solve.
• Check your work: Check your work by plugging the solution back into the original equation to ensure that it is accurate.

Common Mistakes

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

• Forgetting to add or subtract: Forgetting to add or subtract a term from both sides of the equation can lead to an incorrect solution.
• Not combining like terms: Not combining like terms can make the equation more difficult to solve and increase the risk of error.
• Not checking your work: Not checking your work can lead to an incorrect solution and undermine the accuracy of the solution.

Conclusion

Solving linear equations is an essential skill in mathematics, and showing all calculations is a crucial aspect of problem-solving. By following the steps outlined in this article, we can solve linear equations with one variable and ensure that our solutions are accurate. With practice and patience, we can master the art of solving linear equations and apply it to real-world applications.

Introduction

Solving linear equations is a fundamental concept in mathematics, and it's essential to understand the steps involved in solving these equations. In this article, we will provide a Q&A guide to help you understand the process of solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (usually x) is 1. It can be written in the form ax + b = c, where a, b, and c are constants.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable (usually x) on one side of the equation. You can do this by using inverse operations, such as addition, subtraction, multiplication, and division.

Q: What are inverse operations?

A: Inverse operations are operations that "undo" each other. For example, addition and subtraction are inverse operations, as are multiplication and division.

Q: How do I use inverse operations to solve a linear equation?

A: To use inverse operations to solve a linear equation, you need to apply the inverse operation to both sides of the equation. For example, if you have the equation 2x + 3 = 5, you can subtract 3 from both sides to get 2x = 2.

Q: What if I have a fraction in my linear equation?

A: If you have a fraction in your linear equation, you can multiply both sides of the equation by the denominator of the fraction to eliminate the fraction. For example, if you have the equation x/2 = 3, you can multiply both sides by 2 to get x = 6.

Q: What if I have a negative number in my linear equation?

A: If you have a negative number in your linear equation, you can multiply both sides of the equation by -1 to eliminate the negative sign. For example, if you have the equation -x = 3, you can multiply both sides by -1 to get x = -3.

Q: How do I check my work when solving a linear equation?

A: To check your work when solving a linear equation, you need to plug your solution back into the original equation to make sure it is true. For example, if you have the equation 2x + 3 = 5 and you solve for x, you can plug your solution back into the equation to make sure it is true.

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

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

• Forgetting to add or subtract a term from both sides of the equation
• Not combining like terms
• Not checking your work
• Not using inverse operations correctly

Q: How can I practice solving linear equations?

A: You can practice solving linear equations by working through examples and exercises in a textbook or online resource. You can also try solving linear equations on your own by creating your own problems and solutions.

Q: What are some real-world applications of linear equations?

A: Linear equations have many real-world applications, including:

• Finance: Linear equations can be used to calculate interest rates, investment returns, and other financial metrics.
• Science: Linear equations can be used to model population growth, chemical reactions, and other scientific phenomena.
• Engineering: Linear equations can be used to design and optimize systems, including electrical circuits, mechanical systems, and other engineering applications.

Conclusion

Solving linear equations is an essential skill in mathematics, and it's essential to understand the steps involved in solving these equations. By following the steps outlined in this article and practicing regularly, you can become proficient in solving linear equations and apply it to real-world applications.