Solve For $x$:$2x + 7 = 21$Simplify Your Answer As Much As Possible.

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 simple linear equation of the form $2x + 7 = 21$. We will break down the solution into step-by-step instructions, making it easy to understand and follow.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable (in this case, $x$) is 1. It can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants. Linear equations can be solved using various methods, including algebraic manipulation and graphical methods.

The Equation to Solve

The equation we will be solving is $2x + 7 = 21$. This is a simple linear equation, and we will use algebraic manipulation to solve for $x$.

Step 1: Subtract 7 from Both Sides

To solve for $x$, we need to isolate the variable on one side of the equation. The first step is to subtract 7 from both sides of the equation. This will eliminate the constant term on the left-hand side.

$$2x + 7 - 7 = 21 - 7$$

$$2x = 14$$

Step 2: Divide Both Sides by 2

Now that we have $2x = 14$, we need to isolate $x$ by dividing both sides of the equation by 2. This will give us the value of $x$.

$$\frac{2x}{2} = \frac{14}{2}$$

$$x = 7$$

Conclusion

We have successfully solved the linear equation $2x + 7 = 21$ by following a step-by-step approach. By subtracting 7 from both sides and then dividing both sides by 2, we isolated the variable $x$ and found its value to be 7.

Tips and Tricks

• When solving linear equations, it's essential to follow the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
• Make sure to check your work by plugging the solution back into the original equation.
• If you're struggling to solve a linear equation, try breaking it down into smaller steps or using a different method, such as graphing.

Real-World Applications

Linear equations have numerous real-world applications, including:

• Physics: Linear equations are used to describe the motion of objects under constant acceleration.
• Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
• Economics: Linear equations are used to model economic systems and make predictions about future trends.

Common Mistakes to Avoid

• Not following the order of operations (PEMDAS).
• Not checking your work by plugging the solution back into the original equation.
• Not using a consistent method for solving linear equations.

Conclusion

Introduction

In our previous article, we explored the basics of solving linear equations, including the step-by-step process for solving a simple linear equation of the form $2x + 7 = 21$. In this article, we will answer some of the most frequently asked questions about solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (in this case, $x$) is 1. It can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants.

Q: How do I know if an equation is linear?

A: To determine if an equation is linear, look for the following characteristics:

• The highest power of the variable is 1.
• The equation can be written in the form $ax + b = c$.
• The equation can be graphed as a straight line.

Q: What are some common types of linear equations?

A: Some common types of linear equations include:

• Simple linear equations: Equations of the form $ax + b = c$, where $a$, $b$, and $c$ are constants.
• Multi-variable linear equations: Equations of the form $ax + by + cz = d$, where $a$, $b$, $c$, and $d$ are constants.
• Systems of linear equations: Sets of two or more linear equations that are solved simultaneously.

Q: How do I solve a linear equation with fractions?

A: To solve a linear equation with fractions, follow these steps:

1. Multiply both sides of the equation by the least common multiple (LCM) of the denominators.
2. Simplify the equation by canceling out any common factors.
3. Solve the equation using the standard method for solving linear equations.

Q: Can I use a calculator to solve linear equations?

A: Yes, you can use a calculator to solve linear equations. However, it's essential to understand the underlying math and be able to verify the solution using algebraic manipulation.

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

• Not following the order of operations (PEMDAS).
• Not checking your work by plugging the solution back into the original equation.
• Not using a consistent method for solving linear equations.

Q: How do I graph a linear equation?

A: To graph a linear equation, follow these steps:

1. Determine the slope and y-intercept of the equation.
2. Plot the y-intercept on the coordinate plane.
3. Use the slope to plot additional points on the line.
4. Draw a line through the points to represent the equation.

Q: Can I use linear equations to model real-world problems?

A: Yes, linear equations can be used to model a wide range of real-world problems, including:

• Physics: Linear equations are used to describe the motion of objects under constant acceleration.
• Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
• Economics: Linear equations are used to model economic systems and make predictions about future trends.

Conclusion

Solving linear equations is a fundamental skill that is essential for success in mathematics and other fields. By understanding the basics of linear equations and practicing with real-world examples, you can develop the skills and confidence you need to tackle even the most complex linear equations.