What Is The Solution To This Equation? X + 15 = 28 X + 15 = 28 X + 15 = 28 A. X = 13 X = 13 X = 13 B. X = 23 X = 23 X = 23 C. X = 43 X = 43 X = 43 D. X = 33 X = 33 X = 33

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will focus on solving a simple linear equation, $x + 15 = 28$, and explore the different methods and techniques used to find the solution.

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 is a simple equation that can be solved using basic algebraic operations. Linear equations can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants.

The Equation $x + 15 = 28$

The equation $x + 15 = 28$ is a simple linear equation that can be solved using basic algebraic operations. To solve this equation, we need to isolate the variable $x$ on one side of the equation.

Step 1: Subtract 15 from Both Sides

To isolate the variable $x$, we need to subtract 15 from both sides of the equation. This will give us:

$x + 15 - 15 = 28 - 15$

Simplifying the equation, we get:

$x = 13$

Step 2: Check the Solution

To verify that the solution is correct, we can plug it back into the original equation:

$x + 15 = 28$

Substituting $x = 13$ into the equation, we get:

$13 + 15 = 28$

Simplifying the equation, we get:

$28 = 28$

This confirms that the solution $x = 13$ is correct.

Conclusion

In this article, we solved the linear equation $x + 15 = 28$ using basic algebraic operations. We isolated the variable $x$ on one side of the equation by subtracting 15 from both sides. We then verified that the solution is correct by plugging it back into the original equation.

Common Mistakes to Avoid

When solving linear equations, there are several common mistakes to avoid:

• Not isolating the variable: Make sure to isolate the variable on one side of the equation.
• Not checking the solution: Verify that the solution is correct by plugging it back into the original equation.
• Not simplifying the equation: Simplify the equation as much as possible to make it easier to solve.

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.

Practice Problems

To practice solving linear equations, try the following problems:

• $x + 20 = 35$
• $x - 10 = 25$
• $x + 5 = 30$

Conclusion

In conclusion, solving linear equations is a crucial skill for students and professionals alike. By following the steps outlined in this article, you can solve linear equations with ease. Remember to isolate the variable, check the solution, and simplify the equation as much as possible. With practice, you will become proficient in solving linear equations and be able to apply them to real-world problems.

Final Answer

The final answer to the equation $x + 15 = 28$ is:

$x = 13$

Answer Choices

The answer choices are:

A. $x = 13$ B. $x = 23$ C. $x = 43$ D. $x = 33$

The correct answer is:

$$

Introduction

In our previous article, we explored the concept of linear equations and solved a simple equation, $x + 15 = 28$. In this article, we will answer some 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 is a simple equation that can be solved using basic algebraic operations.

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. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

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, plug it back into the original equation and simplify. If the equation is true, then your solution is correct.

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

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

• Not isolating the variable
• Not checking the solution
• Not simplifying the equation
• Not following the order of operations

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

A: To solve a linear equation with fractions, you need to eliminate the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators.

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

A: To solve a linear equation with decimals, you need to eliminate the decimals by multiplying both sides of the equation by a power of 10.

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

A: Yes, you can use a calculator to solve linear equations. However, make sure to check your solution by plugging it back into the original equation.

Q: How do I graph a linear equation?

A: To graph a linear equation, you need to plot two points on the graph and draw a line through them. You can also use a graphing calculator to graph the equation.

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

A: 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.

Conclusion

In conclusion, solving linear equations is a crucial skill for students and professionals alike. By following the steps outlined in this article, you can solve linear equations with ease. Remember to isolate the variable, check the solution, and simplify the equation as much as possible. With practice, you will become proficient in solving linear equations and be able to apply them to real-world problems.

Final Answer

The final answer to the equation $x + 15 = 28$ is:

$x = 13$

Answer Choices

The answer choices are:

A. $x = 13$ B. $x = 23$ C. $x = 43$ D. $x = 33$

The correct answer is:

A. $x = 13$