Solve The Equation: $x - 31 = 54 - 2$

$$

Introduction

Mathematics is a fundamental subject that deals with numbers, quantities, and shapes. It is a vital tool for problem-solving, critical thinking, and logical reasoning. In mathematics, equations are used to represent relationships between variables, and solving them is an essential skill for students and professionals alike. In this article, we will focus on solving a simple equation: $x - 31 = 54 - 2$. We will break down the steps involved in solving this equation and provide a clear explanation of the process.

Understanding the Equation

The given equation is $x - 31 = 54 - 2$. To solve this equation, we need to isolate the variable $x$ on one side of the equation. The equation consists of two parts: $x - 31$ and $54 - 2$. Our goal is to simplify the equation and find the value of $x$.

Step 1: Simplify the Right-Hand Side

The first step is to simplify the right-hand side of the equation by evaluating the expression $54 - 2$. This is a simple subtraction problem, and the result is $52$. So, the equation becomes:

$x - 31 = 52$

Step 2: Add 31 to Both Sides

The next step is to add 31 to both sides of the equation to isolate the variable $x$. This will eliminate the negative term on the left-hand side. When we add 31 to both sides, we get:

$x - 31 + 31 = 52 + 31$

Simplifying the left-hand side, we get:

$x = 83$

Step 3: Verify the Solution

To verify the solution, we can plug the value of $x$ back into the original equation. If the equation holds true, then our solution is correct. Substituting $x = 83$ into the original equation, we get:

$83 - 31 = 54 - 2$

Simplifying both sides, we get:

$52 = 52$

This confirms that our solution is correct.

Conclusion

Solving the equation $x - 31 = 54 - 2$ involves simplifying the right-hand side, adding 31 to both sides, and verifying the solution. By following these steps, we can isolate the variable $x$ and find its value. This equation is a simple example of how to solve linear equations, and the steps involved can be applied to more complex equations as well.

Tips and Tricks

• When solving equations, it's essential to simplify the right-hand side first.
• Adding or subtracting the same value to both sides of an equation is a common technique used to isolate the variable.
• Verifying the solution by plugging the value back into the original equation is a crucial step to ensure that the solution is correct.

Real-World Applications

Solving equations is a fundamental skill that has numerous real-world applications. In mathematics, equations are used to model real-world problems, such as:

• Physics: Equations are used to describe the motion of objects, forces, and energies.
• Engineering: Equations are used to design and optimize systems, such as bridges, buildings, and electronic circuits.
• Economics: Equations are used to model economic systems, such as supply and demand, inflation, and unemployment.

Common Mistakes

• Failing to simplify the right-hand side of the equation.
• Adding or subtracting the wrong value to both sides of the equation.
• Not verifying the solution by plugging the value back into the original equation.

Conclusion

$$$$ $$

Introduction

In our previous article, we solved the equation $x - 31 = 54 - 2$ and found the value of $x$ to be 83. However, we understand that some readers may still have questions or doubts about the solution. In this article, we will address some of the most frequently asked questions (FAQs) about solving this equation.

Q: What is the first step in solving the equation $x - 31 = 54 - 2$?

A: The first step in solving the equation $x - 31 = 54 - 2$ is to simplify the right-hand side of the equation by evaluating the expression $54 - 2$. This is a simple subtraction problem, and the result is $52$. So, the equation becomes:

$x - 31 = 52$

Q: Why do we need to add 31 to both sides of the equation?

A: We need to add 31 to both sides of the equation to eliminate the negative term on the left-hand side. When we add 31 to both sides, we get:

$x - 31 + 31 = 52 + 31$

Simplifying the left-hand side, we get:

$x = 83$

Q: How do we verify the solution?

A: To verify the solution, we can plug the value of $x$ back into the original equation. If the equation holds true, then our solution is correct. Substituting $x = 83$ into the original equation, we get:

$83 - 31 = 54 - 2$

Simplifying both sides, we get:

$52 = 52$

This confirms that our solution is correct.

Q: What if the equation has multiple variables?

A: If the equation has multiple variables, we need to isolate one variable at a time. We can use the same steps as before, but we need to be careful not to confuse the variables. For example, if we have the equation $x + y = 10$, we can isolate $x$ by subtracting $y$ from both sides:

$x + y - y = 10 - y$

Simplifying the left-hand side, we get:

$x = 10 - y$

Q: Can we use algebraic manipulations to solve the equation?

A: Yes, we can use algebraic manipulations to solve the equation. For example, if we have the equation $x - 31 = 54 - 2$, we can add 31 to both sides to get:

$x = 52 + 31$

Simplifying the right-hand side, we get:

$x = 83$

Q: What if the equation has fractions or decimals?

A: If the equation has fractions or decimals, we need to be careful when simplifying the right-hand side. For example, if we have the equation $x - 31 = 54 - 2.5$, we can simplify the right-hand side by evaluating the expression $54 - 2.5$. This is a simple subtraction problem, and the result is $51.5$. So, the equation becomes:

$x - 31 = 51.5$

We can then add 31 to both sides to get:

$x = 51.5 + 31$

Simplifying the right-hand side, we get:

$x = 82.5$

Conclusion

Solving the equation $x - 31 = 54 - 2$ is a simple example of how to solve linear equations. By following the steps involved, we can isolate the variable $x$ and find its value. This equation is a fundamental concept in mathematics, and the skills learned can be applied to more complex equations and real-world problems. We hope that this Q&A article has helped to clarify any doubts or questions you may have had about solving this equation.