Solve: 3 ( 4 P + 3 ) + 4 = 37 3(4p + 3) + 4 = 37 3 ( 4 P + 3 ) + 4 = 37 P = □ P = \square P = □

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Introduction

Mathematics is a subject that deals with numbers, quantities, and shapes. It is a fundamental subject that is used in various fields such as science, technology, engineering, and mathematics (STEM). In mathematics, there are various types of problems that need to be solved, and one of the most common types of problems is algebraic equations. Algebraic equations are equations that contain variables and constants, and they need to be solved to find the value of the variable. In this article, we will solve an algebraic equation, $3(4p + 3) + 4 = 37$, to find the value of the variable $p$.

Understanding the Equation

The given equation is $3(4p + 3) + 4 = 37$. This equation is a linear equation, which means it is an equation that can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable. In this equation, the variable is $p$, and the constants are $3$, $4$, and $37$. The equation can be simplified by using the distributive property, which states that $a(b + c) = ab + ac$. Using this property, we can simplify the equation as follows:

$3(4p + 3) + 4 = 37$

$12p + 9 + 4 = 37$

$12p + 13 = 37$

Solving the Equation

Now that we have simplified the equation, we can solve it to find the value of the variable $p$. To solve the equation, we need to isolate the variable $p$ on one side of the equation. We can do this by subtracting $13$ from both sides of the equation, which gives us:

$12p + 13 - 13 = 37 - 13$

$12p = 24$

Isolating the Variable

Now that we have isolated the variable $p$ on one side of the equation, we can solve for $p$ by dividing both sides of the equation by $12$. This gives us:

$12p / 12 = 24 / 12$

$p = 2$

Conclusion

In this article, we solved an algebraic equation, $3(4p + 3) + 4 = 37$, to find the value of the variable $p$. We simplified the equation using the distributive property, and then solved it by isolating the variable $p$ on one side of the equation. We found that the value of $p$ is $2$. This problem is an example of how algebraic equations can be solved to find the value of a variable.

Importance of Algebraic Equations

Algebraic equations are an important part of mathematics, and they have many real-world applications. They are used in various fields such as science, technology, engineering, and mathematics (STEM). Algebraic equations are used to model real-world problems, and they are used to make predictions and decisions. In this article, we solved an algebraic equation to find the value of a variable, which is an example of how algebraic equations can be used to solve real-world problems.

Real-World Applications of Algebraic Equations

Algebraic equations have many real-world applications. They are used in various fields such as science, technology, engineering, and mathematics (STEM). Some examples of real-world applications of algebraic equations include:

• Physics: Algebraic equations are used to model the motion of objects, and they are used to make predictions about the behavior of objects.
• Engineering: Algebraic equations are used to design and optimize systems, and they are used to make predictions about the behavior of systems.
• Computer Science: Algebraic equations are used to model the behavior of computer systems, and they are used to make predictions about the behavior of computer systems.
• Economics: Algebraic equations are used to model the behavior of economic systems, and they are used to make predictions about the behavior of economic systems.

Tips for Solving Algebraic Equations

Solving algebraic equations can be challenging, but there are some tips that can help. Here are some tips for solving algebraic equations:

• Read the equation carefully: Before solving the equation, read it carefully to make sure you understand what it is asking for.
• Simplify the equation: Simplify the equation by using the distributive property and combining like terms.
• Isolate the variable: Isolate the variable on one side of the equation by adding, subtracting, multiplying, or dividing both sides of the equation.
• Check your answer: Check your answer by plugging it back into the original equation to make sure it is true.

Conclusion

In this article, we solved an algebraic equation, $3(4p + 3) + 4 = 37$, to find the value of the variable $p$. We simplified the equation using the distributive property, and then solved it by isolating the variable $p$ on one side of the equation. We found that the value of $p$ is $2$. This problem is an example of how algebraic equations can be solved to find the value of a variable. Algebraic equations have many real-world applications, and they are used in various fields such as science, technology, engineering, and mathematics (STEM).

Introduction

Algebraic equations are a fundamental concept in mathematics, and they have many real-world applications. In our previous article, we solved an algebraic equation, $3(4p + 3) + 4 = 37$, to find the value of the variable $p$. In this article, we will answer some frequently asked questions about algebraic equations.

Q&A

Q: What is an algebraic equation?

A: An algebraic equation is an equation that contains variables and constants. It is a statement that says two expressions are equal, and it can be used to solve for the value of a variable.

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

A: A linear equation is an equation that can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable. A quadratic equation is an equation that can be written in the form $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable on one side of the equation. You can do this by adding, subtracting, multiplying, or dividing both sides of the equation.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you need to use the quadratic formula, which is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. This formula will give you two solutions for the value of the variable.

Q: What is the distributive property?

A: The distributive property is a rule that states that $a(b + c) = ab + ac$. This means that you can multiply a single term by two or more terms, and then add or subtract the results.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to combine like terms. Like terms are terms that have the same variable and exponent. You can combine like terms by adding or subtracting their coefficients.

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 you have multiple operations in an expression. 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 answer?

A: To check your answer, you need to plug it back into the original equation to make sure it is true. If the equation is true, then your answer is correct.

Conclusion

Algebraic equations are a fundamental concept in mathematics, and they have many real-world applications. In this article, we answered some frequently asked questions about algebraic equations. We hope that this article has been helpful in understanding algebraic equations and how to solve them.

Tips for Solving Algebraic Equations

Here are some tips for solving algebraic equations:

• Read the equation carefully: Before solving the equation, read it carefully to make sure you understand what it is asking for.
• Simplify the equation: Simplify the equation by using the distributive property and combining like terms.
• Isolate the variable: Isolate the variable on one side of the equation by adding, subtracting, multiplying, or dividing both sides of the equation.
• Check your answer: Check your answer by plugging it back into the original equation to make sure it is true.

Real-World Applications of Algebraic Equations

Algebraic equations have many real-world applications. They are used in various fields such as science, technology, engineering, and mathematics (STEM). Some examples of real-world applications of algebraic equations include:

• Physics: Algebraic equations are used to model the motion of objects, and they are used to make predictions about the behavior of objects.
• Engineering: Algebraic equations are used to design and optimize systems, and they are used to make predictions about the behavior of systems.
• Computer Science: Algebraic equations are used to model the behavior of computer systems, and they are used to make predictions about the behavior of computer systems.
• Economics: Algebraic equations are used to model the behavior of economic systems, and they are used to make predictions about the behavior of economic systems.

Conclusion

In this article, we answered some frequently asked questions about algebraic equations. We hope that this article has been helpful in understanding algebraic equations and how to solve them. Algebraic equations have many real-world applications, and they are used in various fields such as science, technology, engineering, and mathematics (STEM).