Solve For The Variables In The Equation:${ 43 + 39 + 2b = 108 + T }$

Introduction

In mathematics, equations are a fundamental concept that helps us understand and describe various relationships between variables. Solving for variables in equations is a crucial skill that is essential in mathematics, science, and engineering. In this article, we will focus on solving for variables in linear equations, specifically the equation: $43 + 39 + 2b = 108 + t$. We will break down the solution step by step and provide a clear explanation of each step.

Understanding the Equation

The given equation is: $43 + 39 + 2b = 108 + t$. This equation is a linear equation, which means it can be written in the form of $ax + by = c$, where $a$, $b$, and $c$ are constants, and $x$ and $y$ are variables.

Step 1: Simplify the Equation

To simplify the equation, we need to combine like terms on both sides of the equation. On the left-hand side, we have $43 + 39$, which can be combined to get $82$. The equation now becomes: $82 + 2b = 108 + t$.

Step 2: Isolate the Variable

To isolate the variable $b$, we need to get rid of the constant term $82$ on the left-hand side. We can do this by subtracting $82$ from both sides of the equation. The equation now becomes: $2b = 108 + t - 82$.

Step 3: Simplify the Right-Hand Side

To simplify the right-hand side, we need to combine like terms. We have $108 - 82$, which can be combined to get $26$. The equation now becomes: $2b = 26 + t$.

Step 4: Isolate the Variable b

To isolate the variable $b$, we need to get rid of the constant term $26$ on the right-hand side. We can do this by subtracting $26$ from both sides of the equation. The equation now becomes: $2b - 26 = t$.

Step 5: Solve for b

To solve for $b$, we need to get rid of the coefficient $2$ on the left-hand side. We can do this by dividing both sides of the equation by $2$. The equation now becomes: $b = \frac{t + 26}{2}$.

Conclusion

In this article, we have solved for the variable $b$ in the equation: $43 + 39 + 2b = 108 + t$. We have broken down the solution step by step and provided a clear explanation of each step. We have also simplified the equation and isolated the variable $b$ to get the final solution.

Real-World Applications

Solving for variables in equations has many real-world applications. For example, in physics, we can use equations to describe the motion of objects. In economics, we can use equations to model the behavior of markets. In engineering, we can use equations to design and optimize systems.

Tips and Tricks

Here are some tips and tricks to help you solve for variables in equations:

• Always simplify the equation before solving for the variable.
• Use inverse operations to isolate the variable.
• Check your solution by plugging it back into the original equation.

Common Mistakes

Here are some common mistakes to avoid when solving for variables in equations:

• Not simplifying the equation before solving for the variable.
• Not using inverse operations to isolate the variable.
• Not checking the solution by plugging it back into the original equation.

Conclusion

Introduction

In our previous article, we discussed how to solve for variables in linear equations. In this article, we will provide a Q&A section to help you better understand the concepts and solve for variables in equations.

Q: What is a linear equation?

A: A linear equation is an equation that can be written in the form of $ax + by = c$, where $a$, $b$, and $c$ are constants, and $x$ and $y$ are variables.

Q: How do I simplify a linear equation?

A: To simplify a linear equation, you need to combine like terms on both sides of the equation. This involves adding or subtracting the coefficients of the variables.

Q: What is the inverse operation?

A: The inverse operation is an operation that undoes another operation. For example, if you add 2 to a number, the inverse operation is to subtract 2 from the number.

Q: How do I isolate a variable in a linear equation?

A: To isolate a variable in a linear equation, you need to get rid of the constant term on the same side of the equation as the variable. You can do this by using inverse operations.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when solving 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 check my solution?

A: 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 for variables in equations?

A: Some common mistakes to avoid when solving for variables in equations include:

• Not simplifying the equation before solving for the variable.
• Not using inverse operations to isolate the variable.
• Not checking the solution by plugging it back into the original equation.

Q: How do I solve for variables in equations with fractions?

A: To solve for variables in equations with fractions, you need to follow the same steps as solving for variables in linear equations. However, you will need to use inverse operations to eliminate the fractions.

Q: How do I solve for variables in equations with decimals?

A: To solve for variables in equations with decimals, you need to follow the same steps as solving for variables in linear equations. However, you will need to use inverse operations to eliminate the decimals.

Q: What are some real-world applications of solving for variables in equations?

A: Some real-world applications of solving for variables in equations include:

• Physics: Solving for variables in equations is used to describe the motion of objects.
• Economics: Solving for variables in equations is used to model the behavior of markets.
• Engineering: Solving for variables in equations is used to design and optimize systems.

Conclusion

Solving for variables in equations is a crucial skill that is essential in mathematics, science, and engineering. By following the steps outlined in this article, you can solve for variables in linear equations and apply the concepts to real-world problems. Remember to simplify the equation, use inverse operations to isolate the variable, and check your solution by plugging it back into the original equation.