Solve For \[$x\$\].$\[x - (-15) = 9\\]

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Introduction to Linear Equations

Linear equations are a fundamental concept in mathematics, and they play a crucial role in various fields such as physics, engineering, and economics. A linear equation is an equation in which the highest power of the variable(s) is 1. In this article, we will focus on solving linear equations of the form ax = b, where a and b are constants.

Understanding the Given Equation

The given equation is x - (-15) = 9. To solve for x, we need to isolate the variable x on one side of the equation. The first step is to simplify the equation by removing the negative sign from the term -(-15).

Simplifying the Equation

When we remove the negative sign from -(-15), we get x + 15 = 9. This is because the negative sign of a negative number is equivalent to a positive sign.

Isolating the Variable x

To isolate the variable x, we need to get rid of the constant term 15 on the same side as x. We can do this by subtracting 15 from both sides of the equation.

Subtracting 15 from Both Sides

x + 15 - 15 = 9 - 15

This simplifies to x = -6.

Verifying the Solution

To verify the solution, we can plug x = -6 back into the original equation and check if it satisfies the equation.

x - (-15) = 9 -6 - (-15) = 9 -6 + 15 = 9 9 = 9

Since the equation holds true, we can confirm that x = -6 is the correct solution.

Conclusion

Solving linear equations is an essential skill in mathematics, and it requires a step-by-step approach. By following the steps outlined in this article, we can solve linear equations of the form ax = b. Remember to simplify the equation, isolate the variable x, and verify the solution to ensure that it satisfies the original equation.

Frequently Asked Questions

  • What is a linear equation? A linear equation is an equation in which the highest power of the variable(s) is 1.
  • How do I solve a linear equation? To solve a linear equation, you need to isolate the variable x on one side of the equation by simplifying the equation, removing constants, and verifying the solution.
  • What is the difference between a linear equation and a quadratic equation? A linear equation has the highest power of the variable(s) as 1, while a quadratic equation has the highest power of the variable(s) as 2.

Real-World Applications of Linear Equations

Linear equations have numerous real-world applications in various fields such as:

  • 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.

Tips and Tricks for Solving Linear Equations

  • Always simplify the equation before solving it.
  • Use inverse operations to isolate the variable x.
  • Verify the solution by plugging it back into the original equation.
  • Practice solving linear equations to become proficient in this skill.

Common Mistakes to Avoid

  • Not simplifying the equation before solving it.
  • Not using inverse operations to isolate the variable x.
  • Not verifying the solution by plugging it back into the original equation.
  • Not practicing solving linear equations to become proficient in this skill.

Conclusion

Solving linear equations is a fundamental skill in mathematics that has numerous real-world applications. By following the steps outlined in this article, you can solve linear equations of the form ax = b. Remember to simplify the equation, isolate the variable x, and verify the solution to ensure that it satisfies the original equation. With practice and patience, you can become proficient in solving linear equations and apply this skill to various fields.