Solve The Equation. Check The Solution.$2x - 10 = 18$x = \square$ (Simplify Your Answer.)

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, $2x - 10 = 18$, and provide a step-by-step guide on how to check the solution.

Understanding Linear Equations

A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, 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. Linear equations can be solved using various methods, including addition, subtraction, multiplication, and division.

Solving the Equation

To solve the equation $2x - 10 = 18$, we need to isolate the variable $x$. We can do this by adding 10 to both sides of the equation, which will eliminate the negative term.

Step 1: Add 10 to Both Sides

$2x - 10 + 10 = 18 + 10$

This simplifies to:

$2x = 28$

Step 2: Divide Both Sides by 2

$\frac{2x}{2} = \frac{28}{2}$

This simplifies to:

$x = 14$

Checking the Solution

To check the solution, we need to substitute the value of $x$ back into the original equation and verify that it is true.

Step 1: Substitute $x = 14$ into the Original Equation

$2(14) - 10 = 18$

This simplifies to:

$28 - 10 = 18$

Step 2: Simplify the Equation

$18 = 18$

Since the equation is true, we can conclude that the solution is correct.

Conclusion

Solving linear equations is an essential skill for students to master. By following the steps outlined in this article, we can solve simple linear equations like $2x - 10 = 18$ and check the solution. Remember to always add or subtract the same value to both sides of the equation, and to multiply or divide both sides by the same value. With practice and patience, you will become proficient in solving linear equations and be able to tackle more complex equations with confidence.

Tips and Tricks

• Always read the equation carefully and identify the variable(s) and constants.
• Use addition, subtraction, multiplication, and division to isolate the variable(s).
• Check the solution by substituting the value of the variable(s) back into the original equation.
• Practice, practice, practice! The more you practice solving linear equations, the more confident you will become.

Common Mistakes to Avoid

• Not reading the equation carefully and making mistakes when isolating the variable(s).
• Not checking the solution by substituting the value of the variable(s) back into the original equation.
• Not using the correct order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).

Real-World Applications

Linear equations have numerous real-world applications, including:

• Physics: Linear equations are used to describe the motion of objects and the forces acting on them.
• 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

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Introduction

In our previous article, we discussed how to solve linear equations using a step-by-step guide. In this article, we will provide a Q&A guide to help you better understand the concept of solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, 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.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable(s) 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 PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. This means that you need to perform operations inside parentheses first, followed by exponents, then multiplication and division, and finally addition and subtraction.

Q: How do I check the solution?

A: To check the solution, you need to substitute the value of the variable(s) back into the original equation and verify that it is true.

Q: What are some common mistakes to avoid?

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

• Not reading the equation carefully and making mistakes when isolating the variable(s).
• Not checking the solution by substituting the value of the variable(s) back into the original equation.
• Not using the correct order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).

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 and the forces acting on them.
• 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.

Q: How can I practice solving linear equations?

A: You can practice solving linear equations by:

• Working on sample problems and exercises.
• Using online resources and tools, such as calculators and software.
• Joining a study group or working with a tutor.

Q: What are some tips for solving linear equations?

A: Some tips for solving linear equations include:

• Read the equation carefully and identify the variable(s) and constants.
• Use addition, subtraction, multiplication, and division to isolate the variable(s).
• Check the solution by substituting the value of the variable(s) back into the original equation.
• Practice regularly to become proficient in solving linear equations.

Conclusion

Solving linear equations is a fundamental skill that has numerous real-world applications. By following the steps outlined in this article and practicing regularly, you can become proficient in solving linear equations and apply them to real-world problems.

Additional Resources

• Online resources: Khan Academy, Mathway, and Wolfram Alpha.
• Textbooks: Algebra and Geometry.
• Study groups: Join a study group or work with a tutor to practice solving linear equations.

Common Linear Equation Problems

• $2x - 10 = 18$
• $x + 5 = 12$
• $3x - 2 = 14$
• $x - 3 = 7$

Solving Linear Equations: A Final Tip

• Always read the equation carefully and identify the variable(s) and constants.
• Use addition, subtraction, multiplication, and division to isolate the variable(s).
• Check the solution by substituting the value of the variable(s) back into the original equation.
• Practice regularly to become proficient in solving linear equations.