Follow The Steps To Solve This Equation:$\[ 3(2x + 6) - 4x = 2(5x - 2) + 6 \\]1. Use The Distributive Property: $\[ 6x + 18 - 4x = 10x - 4 + 6 \\]2. Combine Like Terms: $\[ 2x + 18 = 10x + 2 \\]3. Use The Subtraction

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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 guide you through the steps to solve a linear equation using the distributive property, combining like terms, and subtraction. By following these steps, you will be able to solve linear equations with ease and confidence.

Step 1: Use the Distributive Property

The distributive property is a fundamental concept in algebra that allows us to expand expressions with parentheses. In the given equation, we have:

3(2x+6)−4x=2(5x−2)+6{ 3(2x + 6) - 4x = 2(5x - 2) + 6 }

To use the distributive property, we need to multiply the numbers outside the parentheses with the terms inside the parentheses. This will give us:

6x+18−4x=10x−4+6{ 6x + 18 - 4x = 10x - 4 + 6 }

Notice how the distributive property has helped us to expand the expressions and simplify the equation.

Step 2: Combine Like Terms

Now that we have expanded the expressions, we can combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have:

6x−4x=10x{ 6x - 4x = 10x }

And:

18=6{ 18 = 6 }

Combining these like terms, we get:

2x+18=10x+2{ 2x + 18 = 10x + 2 }

Step 3: Use Subtraction

Now that we have combined like terms, we can use subtraction to isolate the variable. To do this, we need to get all the terms with the variable on one side of the equation and the constant terms on the other side. We can do this by subtracting 10x from both sides of the equation:

2x−10x+18=10x−10x+2{ 2x - 10x + 18 = 10x - 10x + 2 }

This simplifies to:

−8x+18=2{ -8x + 18 = 2 }

Step 4: Solve for x

Now that we have isolated the variable, we can solve for x. To do this, we need to get rid of the constant term on the same side as the variable. We can do this by subtracting 18 from both sides of the equation:

−8x=−16{ -8x = -16 }

Now, we can divide both sides of the equation by -8 to solve for x:

x=−16−8{ x = \frac{-16}{-8} }

x=2{ x = 2 }

Conclusion

Solving linear equations is a crucial skill for students to master. By following the steps outlined in this article, you will be able to solve linear equations with ease and confidence. Remember to use the distributive property, combine like terms, and use subtraction to isolate the variable. With practice and patience, you will become proficient in solving linear equations and be able to tackle more complex math problems.

Tips and Tricks

  • Always use the distributive property to expand expressions with parentheses.
  • Combine like terms to simplify the equation.
  • Use subtraction to isolate the variable.
  • Check your work by plugging the solution back into the original equation.

Common Mistakes

  • Failing to use the distributive property.
  • Not combining like terms.
  • Not using subtraction to isolate the variable.
  • Not checking the solution.

Real-World Applications

Solving linear equations has many real-world applications, including:

  • Finance: Solving linear equations can help you calculate interest rates, investments, and loans.
  • Science: Solving linear equations can help you model population growth, chemical reactions, and physical systems.
  • Engineering: Solving linear equations can help you design and optimize systems, such as bridges, buildings, and electronic circuits.

Practice Problems

Try solving the following linear equations using the steps outlined in this article:

  1. 2x + 5 = 11
  2. x - 3 = 7
  3. 4x + 2 = 14

Answer Key

  1. x = 3
  2. x = 10
  3. x = 3

Introduction

Solving linear equations is a crucial skill for students to master. In our previous article, we provided a step-by-step guide on how to solve linear equations using the distributive property, combining like terms, and subtraction. 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 is 1. It is a simple equation that can be solved using basic algebraic operations.

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that allows us to expand expressions with parentheses. It states that for any numbers a, b, and c:

a(b + c) = ab + ac

Q: How do I use the distributive property to solve a linear equation?

A: To use the distributive property to solve a linear equation, you need to multiply the numbers outside the parentheses with the terms inside the parentheses. This will help you expand the expressions and simplify the equation.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, 2x and 4x are like terms because they both have the variable x raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the like terms. For example, if you have 2x + 4x, you can combine them by adding the coefficients:

2x + 4x = 6x

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, you need to plug the solution back into the original equation and see if it is true. If the solution satisfies the equation, then it 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:

  • Failing to use the distributive property.
  • Not combining like terms.
  • Not using subtraction to isolate the variable.
  • Not checking the solution.

Q: How do I apply linear equations to real-world problems?

A: Linear equations have many real-world applications, including finance, science, and engineering. To apply linear equations to real-world problems, you need to identify the variables and the relationships between them, and then use algebraic operations to solve for the unknowns.

Q: What are some tips and tricks for solving linear equations?

A: Some tips and tricks for solving linear equations include:

  • Always use the distributive property to expand expressions with parentheses.
  • Combine like terms to simplify the equation.
  • Use subtraction to isolate the variable.
  • Check your work by plugging the solution back into the original equation.

Conclusion

Solving linear equations is a crucial skill for students to master. By following the steps outlined in this article and practicing with real-world examples, you will become proficient in solving linear equations and be able to tackle more complex math problems. Remember to use the distributive property, combine like terms, and use subtraction to isolate the variable. With practice and patience, you will become proficient in solving linear equations and be able to apply them to real-world problems.