Solve $25 = X + 6.5$. X = X = X =

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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 focus on solving a simple linear equation, $25 = x + 6.5$, to find the value of xx. 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(s) is 1. In other words, it is an equation that can be written in the form ax+b=cax + b = c, where aa, bb, and cc are constants, and xx is the variable. 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 $25 = x + 6.5$. This is a simple linear equation, and we will use algebraic manipulation to solve for xx.

Step 1: Isolate the Variable

To solve for xx, we need to isolate the variable on one side of the equation. In this case, we can subtract 6.5 from both sides of the equation to isolate xx.

25−6.5=x+6.5−6.525 - 6.5 = x + 6.5 - 6.5

This simplifies to:

18.5=x18.5 = x

Step 2: Check the Solution

To ensure that our solution is correct, we can plug it back into the original equation and check if it is true.

25=18.5+6.525 = 18.5 + 6.5

This simplifies to:

25=2525 = 25

Since the equation is true, we can be confident that our solution is correct.

Conclusion

Solving linear equations is an essential skill for students to master. By following the step-by-step instructions outlined in this article, we were able to solve the equation $25 = x + 6.5$ and find the value of xx. Remember to always isolate the variable on one side of the equation and check your solution to ensure that it is correct.

Tips and Tricks

  • When solving linear equations, always follow the order of operations (PEMDAS).
  • Use algebraic manipulation to isolate the variable on one side of the equation.
  • Check your solution by plugging it back into the original equation.

Common Mistakes to Avoid

  • Not isolating the variable on one side of the equation.
  • Not checking the solution to ensure that it is correct.

Real-World Applications

Linear equations have many real-world applications, including:

  • Finance: Linear equations can be used to calculate interest rates and investment returns.
  • Science: Linear equations can be used to model population growth and decay.
  • Engineering: Linear equations can be used to design and optimize systems.

Conclusion

Introduction

In our previous article, we discussed how to solve a simple linear equation, $25 = x + 6.5$. In this article, we will answer some common questions that students often have when it comes to 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=cax + b = c, where aa, bb, and cc are constants, and xx is the variable.

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 see if it is true. 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 on one side of the equation.
  • Not checking the solution to ensure that it is correct.
  • Not following the order of operations.

Q: How do I use linear equations in real-world applications?

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

  • Finance: Linear equations can be used to calculate interest rates and investment returns.
  • Science: Linear equations can be used to model population growth and decay.
  • Engineering: Linear equations can be used to design and optimize systems.

Q: What are some examples of linear equations?

A: Some examples of linear equations include:

  • 2x+3=52x + 3 = 5

  • x−2=3x - 2 = 3

  • 4x=124x = 12

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 can multiply both sides of the equation by 10 to eliminate the decimals.

Conclusion

Solving linear equations is a fundamental skill that has many real-world applications. By following the step-by-step instructions outlined in this article, you can master the art of solving linear equations and apply it to a wide range of problems. Remember to always isolate the variable on one side of the equation and check your solution to ensure that it is correct.

Additional Resources

  • Khan Academy: Linear Equations
  • Mathway: Linear Equations
  • Wolfram Alpha: Linear Equations

Practice Problems

  • Solve the equation $3x + 2 = 7$.
  • Solve the equation $x - 4 = 2$.
  • Solve the equation $2x = 10$.

Answer Key

  • 3x + 2 = 7$: $x = 5/3

  • x - 4 = 2$: $x = 6

  • 2x = 10$: $x = 5