Determine The Value Of \[$ H \$\].1. \[$ 2(3-h) - 6 = -5h \$\]

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Introduction

In mathematics, solving linear equations is a fundamental concept that helps us find the value of unknown variables. In this article, we will focus on solving a specific linear equation, 2(3-h) - 6 = -5h, to determine the value of h. We will break down the solution into manageable steps, making it easy to understand and follow.

Understanding the Equation

The given equation is 2(3-h) - 6 = -5h. To solve for h, we need to isolate the variable h on one side of the equation. Let's start by simplifying the equation.

Simplifying the Equation

The equation 2(3-h) - 6 = -5h can be simplified by distributing the 2 to the terms inside the parentheses.

2(3-h) - 6 = -5h
6 - 2h - 6 = -5h
-2h = -5h

However, we can see that the equation is still not simplified. We need to get rid of the -5h term on the right-hand side of the equation.

Isolating the Variable h

To isolate the variable h, we need to get rid of the -5h term on the right-hand side of the equation. We can do this by adding 5h to both sides of the equation.

-2h = -5h
-2h + 5h = -5h + 5h
3h = 0

Now, we have isolated the variable h on one side of the equation. However, we still need to solve for h.

Solving for h

To solve for h, we need to get rid of the 3 term on the left-hand side of the equation. We can do this by dividing both sides of the equation by 3.

3h = 0
h = 0/3
h = 0

Therefore, the value of h is 0.

Conclusion

In this article, we solved a linear equation, 2(3-h) - 6 = -5h, to determine the value of h. We broke down the solution into manageable steps, making it easy to understand and follow. By simplifying the equation, isolating the variable h, and solving for h, we found that the value of h is 0.

Tips and Tricks

  • When solving linear equations, it's essential to simplify the equation by distributing the terms inside the parentheses.
  • To isolate the variable h, add or subtract the same term to both sides of the equation.
  • To solve for h, divide both sides of the equation by the coefficient of h.

Real-World Applications

Solving linear equations has numerous real-world applications. For example, in physics, linear equations are used to describe the motion of objects. In economics, linear equations are used to model the relationship between variables such as supply and demand. In computer science, linear equations are used to solve systems of linear equations.

Common Mistakes

  • Not simplifying the equation before solving for h.
  • Not isolating the variable h on one side of the equation.
  • Not solving for h by dividing both sides of the equation by the coefficient of h.

Conclusion

Introduction

In our previous article, we solved a linear equation, 2(3-h) - 6 = -5h, to determine the value of h. In this article, we will provide a Q&A guide to help you understand and apply the concepts 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.

Q: How do I simplify a linear equation?

A: To simplify a linear equation, you need to distribute the terms inside the parentheses and combine like terms. For example, in the equation 2(3-h) - 6 = -5h, you would distribute the 2 to the terms inside the parentheses and combine like terms.

Q: How do I isolate the variable h?

A: To isolate the variable h, you need to get rid of the constant term on the same side of the equation as the variable h. You can do this by adding or subtracting the same term to both sides of the equation.

Q: How do I solve for h?

A: To solve for h, you need to get rid of the coefficient of h on the same side of the equation as the variable h. You can do this by dividing both sides of the equation by the coefficient of h.

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

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

  • Not simplifying the equation before solving for h.
  • Not isolating the variable h on one side of the equation.
  • Not solving for h by dividing both sides of the equation by the coefficient of h.

Q: How do I check my solution?

A: To check your solution, you need to plug the value of h back into the original equation and make sure it is true. If the equation is true, then your solution is correct.

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

A: Solving linear equations has numerous real-world applications, including:

  • Physics: Linear equations are used to describe the motion of objects.
  • Economics: Linear equations are used to model the relationship between variables such as supply and demand.
  • Computer Science: Linear equations are used to solve systems of linear equations.

Q: Can you provide an example of a linear equation?

A: Yes, here is an example of a linear equation:

2x + 3 = 5

To solve for x, you would first simplify the equation by distributing the 2 to the terms inside the parentheses:

2x + 3 = 5 2x = 5 - 3 2x = 2

Next, you would isolate the variable x by dividing both sides of the equation by 2:

x = 2/2 x = 1

Therefore, the value of x is 1.

Conclusion

In conclusion, solving linear equations is a fundamental concept in mathematics that helps us find the value of unknown variables. By simplifying the equation, isolating the variable h, and solving for h, we can determine the value of h. Remember to simplify the equation, isolate the variable h, and solve for h to avoid common mistakes.