Solve: $3x + 18 - 7 = 41$A. 10 B. 27 C. 33 D. 52

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 a specific linear equation, $3x + 18 - 7 = 41$, and provide a step-by-step guide on how to arrive at the solution.

Understanding the Equation

Before we dive into solving the equation, let's break it down and understand what it represents. The equation is in the form of $ax + b = c$, where $a$, $b$, and $c$ are constants. In this case, $a = 3$, $b = 18 - 7$, and $c = 41$. Our goal is to isolate the variable $x$ and find its value.

Step 1: Simplify the Equation

The first step in solving the equation is to simplify it by combining like terms. In this case, we can combine the constants on the left-hand side of the equation.

$$3x + 18 - 7 = 41$$

We can simplify the equation by combining the constants:

$$3x + 11 = 41$$

Step 2: Isolate the Variable

Now that we have simplified the equation, we can isolate the variable $x$ by subtracting $11$ from both sides of the equation.

$$3x = 41 - 11$$

$$3x = 30$$

Step 3: Solve for x

Now that we have isolated the variable $x$, we can solve for its value by dividing both sides of the equation by $3$.

$$x = \frac{30}{3}$$

$$x = 10$$

Conclusion

In this article, we have solved the linear equation $3x + 18 - 7 = 41$ using a step-by-step approach. We simplified the equation, isolated the variable $x$, and solved for its value. The solution to the equation is $x = 10$.

Answer

The correct answer is:

• A. 10

Tips and Tricks

• When solving linear equations, it's essential to simplify the equation by combining like terms.
• Isolate the variable by subtracting or adding the same value to both sides of the equation.
• Solve for the variable by dividing both sides of the equation by the coefficient of the variable.

Practice Problems

Try solving the following linear equations:

• $2x + 5 = 11$
• $x - 3 = 7$
• $4x + 2 = 14$

Real-World Applications

Linear equations have numerous real-world applications, including:

• Finance: Linear equations are used to calculate interest rates, investment returns, and loan payments.
• Science: Linear equations are used to model population growth, chemical reactions, and physical phenomena.
• Engineering: Linear equations are used to design and optimize systems, such as bridges, buildings, and electronic circuits.

Conclusion

$$

Introduction

In our previous article, we solved the linear equation $3x + 18 - 7 = 41$ using a step-by-step approach. In this article, we will provide a Q&A guide to help students understand and solve linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable is 1. It is a simple equation that can be solved using basic algebraic operations.

Q: What are the steps to solve a linear equation?

A: The steps to solve a linear equation are:

1. Simplify the equation by combining like terms.
2. Isolate the variable by subtracting or adding the same value to both sides of the equation.
3. Solve for the variable by dividing both sides of the equation by the coefficient of the variable.

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

A: A linear equation is an equation in which the highest power of the variable is 1, while a quadratic equation is an equation in which the highest power of the variable is 2.

Q: How do I simplify a linear equation?

A: To simplify a linear equation, combine like terms by adding or subtracting the coefficients of the same variables.

Q: What is the coefficient of a variable?

A: The coefficient of a variable is the number that is multiplied by the variable. For example, in the equation $2x + 5 = 11$, the coefficient of $x$ is 2.

Q: How do I isolate a variable?

A: To isolate a variable, subtract or add the same value to both sides of the equation. For example, in the equation $2x + 5 = 11$, we can subtract 5 from both sides to isolate the variable $x$.

Q: What is the value of x in the equation 2x + 5 = 11?

A: To solve for $x$, we need to isolate the variable by subtracting 5 from both sides of the equation:

$$2x + 5 - 5 = 11 - 5$$

$$2x = 6$$

$$x = \frac{6}{2}$$

$$x = 3$$

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

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

• Finance: Linear equations are used to calculate interest rates, investment returns, and loan payments.
• Science: Linear equations are used to model population growth, chemical reactions, and physical phenomena.
• Engineering: Linear equations are used to design and optimize systems, such as bridges, buildings, and electronic circuits.

Q: How can I practice solving linear equations?

A: You can practice solving linear equations by working on problems and exercises, such as:

• Solving linear equations with one variable
• Solving linear equations with two variables
• Solving linear equations with fractions and decimals
• Solving linear equations with negative numbers

Conclusion

Solving linear equations is a fundamental skill that has numerous real-world applications. By following a step-by-step approach and practicing regularly, you can become proficient in solving linear equations. In this article, we have provided a Q&A guide to help students understand and solve linear equations.