Solve For \[$ A \$\]:$\[ 4a - 3 = 13 \\]

Introduction

Solving for a variable in an algebraic equation is a fundamental concept in mathematics. In this article, we will focus on solving for the variable $a$ in the given equation $4a - 3 = 13$. This equation is a linear equation, and solving it will involve isolating the variable $a$ on one side of the equation.

Understanding the Equation

The given equation is $4a - 3 = 13$. This equation is a linear equation because it is in the form of $ax + b = c$, where $a$, $b$, and $c$ are constants. In this equation, $a$ is the variable we want to solve for, and the constants are $4$, $-3$, and $13$.

Step 1: Add 3 to Both Sides of the Equation

To solve for $a$, we need to isolate the variable on one side of the equation. The first step is to add 3 to both sides of the equation. This will eliminate the constant term $-3$ on the left side of the equation.

# Given equation: 4a - 3 = 13
# Add 3 to both sides of the equation
# 4a - 3 + 3 = 13 + 3
# 4a = 16

Step 2: Divide Both Sides of the Equation by 4

Now that we have $4a = 16$, we need to isolate the variable $a$ by dividing both sides of the equation by 4. This will give us the value of $a$.

# 4a = 16
# Divide both sides of the equation by 4
# (4a) / 4 = 16 / 4
# a = 4

Conclusion

In this article, we solved for the variable $a$ in the given equation $4a - 3 = 13$. We followed the steps of adding 3 to both sides of the equation and then dividing both sides of the equation by 4 to isolate the variable $a$. The final value of $a$ is 4.

Example Use Case

Solving for a variable in an algebraic equation is a fundamental concept in mathematics. In real-world applications, solving for a variable can help us make predictions, model real-world phenomena, and make informed decisions. For example, in economics, solving for a variable can help us understand the relationship between different economic variables and make predictions about future economic trends.

Tips and Tricks

• When solving for a variable, make sure to follow the order of operations (PEMDAS) to ensure that you are performing the operations in the correct order.
• When adding or subtracting a constant to both sides of the equation, make sure to add or subtract the same value to both sides of the equation.
• When dividing both sides of the equation by a constant, make sure to divide both sides of the equation by the same value.

Frequently Asked Questions

• Q: What is the value of $a$ in the equation $4a - 3 = 13$? A: The value of $a$ is 4.
• Q: How do I solve for a variable in an algebraic equation? A: To solve for a variable, follow the steps of adding or subtracting a constant to both sides of the equation and then dividing both sides of the equation by a constant.
• Q: What is the importance of solving for a variable in an algebraic equation? A: Solving for a variable can help us make predictions, model real-world phenomena, and make informed decisions.

Related Topics

• Solving quadratic equations
• Solving systems of linear equations
• Graphing linear equations
• Solving polynomial equations

References

• [1] "Algebra" by Michael Artin
• [2] "Linear Algebra" by Jim Hefferon
• [3] "Calculus" by Michael Spivak

Note: The references provided are for general information purposes only and are not specific to the topic of solving for a variable in an algebraic equation.

Introduction

In our previous article, we solved for the variable $a$ in the equation $4a - 3 = 13$. In this article, we will provide a Q&A section to address some common questions and concerns related to solving for a variable in an algebraic equation.

Q&A

Q: What is the first step in solving for a variable in an algebraic equation?

A: The first step in solving for a variable in an algebraic equation is to isolate the variable on one side of the equation. This can be done by adding or subtracting a constant to both sides of the equation.

Q: How do I know which operation to perform on the equation?

A: To determine which operation to perform on the equation, you need to identify the variable and the constant term. If the variable is on the same side as the constant term, you can add or subtract the constant term to both sides of the equation. If the variable is on the opposite side of the constant term, you can multiply or divide both sides of the equation by a constant.

Q: What is the difference between adding and subtracting a constant to both sides of the equation?

A: Adding a constant to both sides of the equation is the same as subtracting a negative constant from both sides of the equation. For example, adding 3 to both sides of the equation is the same as subtracting -3 from both sides of the equation.

Q: How do I know when to multiply or divide both sides of the equation by a constant?

A: You should multiply or divide both sides of the equation by a constant when the variable is on the opposite side of the constant term. For example, if the equation is $4a = 16$, you can divide both sides of the equation by 4 to isolate the variable $a$.

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

A: Following the order of operations (PEMDAS) is crucial when solving for a variable in an algebraic equation. It ensures that you perform the operations in the correct order and avoid errors.

Q: Can I use a calculator to solve for a variable in an algebraic equation?

A: Yes, you can use a calculator to solve for a variable in an algebraic equation. However, it's essential to understand the underlying math concepts and be able to solve the equation manually.

Q: How do I check my answer when solving for a variable in an algebraic equation?

A: To check your answer, substitute the value of the variable back into the original equation and verify that it is true. For example, if you solved for $a$ in the equation $4a - 3 = 13$ and got $a = 4$, you can substitute $a = 4$ back into the original equation and verify that it is true.

Tips and Tricks

• Always follow the order of operations (PEMDAS) when solving for a variable in an algebraic equation.
• Use a calculator to check your answer and verify that it is true.
• Practice solving for a variable in different types of algebraic equations to build your skills and confidence.
• Review the underlying math concepts and be able to solve the equation manually.

Frequently Asked Questions

• Q: What is the value of $a$ in the equation $4a - 3 = 13$? A: The value of $a$ is 4.
• Q: How do I solve for a variable in an algebraic equation? A: To solve for a variable, follow the steps of adding or subtracting a constant to both sides of the equation and then multiplying or dividing both sides of the equation by a constant.
• Q: What is the importance of following the order of operations (PEMDAS)? A: Following the order of operations (PEMDAS) is crucial when solving for a variable in an algebraic equation. It ensures that you perform the operations in the correct order and avoid errors.

Related Topics

• Solving quadratic equations
• Solving systems of linear equations
• Graphing linear equations
• Solving polynomial equations

References

• [1] "Algebra" by Michael Artin
• [2] "Linear Algebra" by Jim Hefferon
• [3] "Calculus" by Michael Spivak

Note: The references provided are for general information purposes only and are not specific to the topic of solving for a variable in an algebraic equation.