Solve This Equation: $-9h - 6 + 12h + 40 = 22$.A) $h = 4$ B) $h = -\frac{4}{7}$ C) $h = 24$ D) $h = -4$

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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 specific linear equation, −9h−6+12h+40=22-9h - 6 + 12h + 40 = 22, and explore the different methods and techniques used to arrive at the solution.

Understanding the Equation

The given equation is a linear equation in one variable, hh. It consists of four terms: −9h-9h, −6-6, 12h12h, and 4040. The equation is set equal to 2222, which means that the sum of the four terms on the left-hand side must be equal to 2222.

Step 1: Combine Like Terms

The first step in solving the equation is to combine like terms. In this case, we have two terms with the variable hh, −9h-9h and 12h12h. We can combine these terms by adding their coefficients, which are the numbers in front of the variable.

-9h + 12h = 3h

So, the equation becomes:

3h - 6 + 40 = 22

Step 2: Simplify the Equation

Next, we can simplify the equation by combining the constant terms, −6-6 and 4040. We can do this by adding their values.

-6 + 40 = 34

So, the equation becomes:

3h + 34 = 22

Step 3: Isolate the Variable

Now, we need to isolate the variable hh by getting rid of the constant term, 3434. We can do this by subtracting 3434 from both sides of the equation.

3h + 34 - 34 = 22 - 34

This simplifies to:

3h = -12

Step 4: Solve for the Variable

Finally, we can solve for the variable hh by dividing both sides of the equation by the coefficient of hh, which is 33.

3h / 3 = -12 / 3

This simplifies to:

h = -4

Conclusion

In this article, we have solved the linear equation −9h−6+12h+40=22-9h - 6 + 12h + 40 = 22 using the steps of combining like terms, simplifying the equation, isolating the variable, and solving for the variable. We have arrived at the solution, h=−4h = -4, which is the correct answer.

Answer Options

The answer options are:

A) h=4h = 4 B) h=−47h = -\frac{4}{7} C) h=24h = 24 D) h=−4h = -4

The correct answer is:

D) h=−4h = -4

Discussion

This equation is a simple linear equation, and solving it requires basic algebraic skills. However, it is essential to understand the steps involved in solving linear equations, as they are a fundamental concept in mathematics.

Tips and Tricks

  • When solving linear equations, it is essential to combine like terms and simplify the equation.
  • Isolating the variable is a crucial step in solving linear equations.
  • Solving for the variable requires dividing both sides of the equation by the coefficient of the variable.

Practice Problems

Solving linear equations is a skill that requires practice. Here are some practice problems to help you improve your skills:

  1. Solve the equation 2x+5=112x + 5 = 11.
  2. Solve the equation x−3=7x - 3 = 7.
  3. Solve the equation 4x+2=144x + 2 = 14.

Conclusion

Introduction

In our previous article, we explored the steps involved in solving linear equations. 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. In other words, it is an equation in which the variable is not raised to a power greater than 1.

Q: What are the steps involved in solving a linear equation?

A: The steps involved in solving a linear equation are:

  1. Combine like terms
  2. Simplify the equation
  3. Isolate the variable
  4. Solve for the variable

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable is 1, while a quadratic equation is an equation in which the highest power of the variable is 2.

Q: How do I know if an equation is linear or quadratic?

A: To determine if an equation is linear or quadratic, look at the highest power of the variable. If it is 1, the equation is linear. If it is 2, the equation is quadratic.

Q: What is the coefficient of a variable?

A: The coefficient of a variable is the number in front of the variable. For example, in the equation 2x + 5 = 11, the coefficient of x is 2.

Q: How do I isolate the variable in a linear equation?

A: To isolate the variable in a linear equation, you need to get rid of the constant term by adding or subtracting the same value from both sides of the equation.

Q: What is the difference between adding and subtracting the same value from both sides of an equation?

A: Adding the same value to both sides of an equation is equivalent to subtracting the same value from both sides of the equation. For example, if you add 3 to both sides of the equation x + 2 = 5, you get x + 3 = 8. If you subtract 3 from both sides of the equation x + 2 = 5, you also get x + 3 = 8.

Q: How do I solve for the variable in a linear equation?

A: To solve for the variable in a linear equation, you need to divide both sides of the equation by the coefficient of the variable.

Q: What is the difference between dividing both sides of an equation by a coefficient and dividing both sides of an equation by a constant?

A: Dividing both sides of an equation by a coefficient is equivalent to multiplying both sides of the equation by the reciprocal of the coefficient. For example, if you divide both sides of the equation 2x = 6 by 2, you get x = 3. If you multiply both sides of the equation 2x = 6 by 1/2, you also get x = 3.

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

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

  • Not combining like terms
  • Not simplifying the equation
  • Not isolating the variable
  • Not solving for the variable
  • Dividing both sides of the equation by zero

Conclusion

In conclusion, solving linear equations is a fundamental concept in mathematics, and it requires basic algebraic skills. By following the steps of combining like terms, simplifying the equation, isolating the variable, and solving for the variable, we can arrive at the solution. With practice and patience, you can master the art of solving linear equations.

Practice Problems

Solving linear equations is a skill that requires practice. Here are some practice problems to help you improve your skills:

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

Answer Key

  1. x = 3
  2. x = 10
  3. x = 3.25

Discussion

This article is a Q&A guide to solving linear equations. We have answered some frequently asked questions about solving linear equations and provided some practice problems to help you improve your skills. With practice and patience, you can master the art of solving linear equations.