Solve For { X $} . . . { -5x - 6 = \$}

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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, -5x - 6 = 0, and provide a step-by-step guide on how to isolate the variable x.

Understanding the Equation

A linear equation is an equation in which the highest power of the variable(s) is 1. In this case, we have a single variable, x, and a constant term, -6. The equation is in the form of -5x - 6 = 0, where the goal is to solve for x.

The Importance of Isolating the Variable

Isolating the variable is a crucial step in solving linear equations. It involves getting the variable x by itself on one side of the equation, without any other terms or constants attached to it. In this case, we need to isolate x by getting rid of the constant term, -6.

Step 1: Add 6 to Both Sides of the Equation

To isolate x, we need to get rid of the constant term, -6. We can do this by adding 6 to both sides of the equation. This will cancel out the -6 on the left side, leaving us with just the variable x.

-5x - 6 + 6 = 0 + 6

Step 2: Simplify the Equation

After adding 6 to both sides, we can simplify the equation by combining like terms. In this case, the -6 and +6 cancel each other out, leaving us with just the variable x.

-5x = 6

Step 3: Divide Both Sides by -5

Now that we have the variable x by itself, we need to get rid of the coefficient, -5. We can do this by dividing both sides of the equation by -5. This will give us the value of x.

\frac{-5x}{-5} = \frac{6}{-5}

Step 4: Simplify the Equation

After dividing both sides by -5, we can simplify the equation by canceling out the -5 in the numerator and denominator.

x = -\frac{6}{5}

Conclusion

Solving linear equations is a crucial skill for students to master. By following the steps outlined in this article, we can solve the equation -5x - 6 = 0 and find the value of x. Remember to always isolate the variable, add or subtract constants to both sides, and simplify the equation to find the solution.

Tips and Tricks

  • Always read the equation carefully and identify the variable and constant terms.
  • Use inverse operations to isolate the variable, such as adding or subtracting constants to both sides.
  • Simplify the equation by combining like terms and canceling out coefficients.
  • Check your solution by plugging it back into the original equation.

Real-World Applications

Solving linear equations has many real-world applications, such as:

  • Calculating the cost of goods and services
  • Determining the amount of time it takes to complete a task
  • Finding the area and perimeter of shapes
  • Solving problems in physics, engineering, and other fields

Common Mistakes to Avoid

  • Failing to isolate the variable
  • Adding or subtracting constants to only one side of the equation
  • Not simplifying the equation
  • Not checking the solution

Conclusion

Introduction

In our previous article, we discussed how to solve linear equations, including the equation -5x - 6 = 0. However, we know that practice makes perfect, and sometimes the best way to learn is through asking questions and getting answers. In this article, we will provide a Q&A guide to help you better understand how to solve 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 of ax + b = c, where a, b, and c are constants.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable by getting rid of the constant term. You can do this by adding or subtracting constants to both sides of the equation, and then simplifying the equation.

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(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2. For example, the equation x + 2 = 0 is a linear equation, while the equation x^2 + 4x + 4 = 0 is a quadratic equation.

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

A: To determine if an equation is linear or quadratic, you need to look at the highest power of the variable(s). If the highest power is 1, then the equation is linear. If the highest power is 2, then the equation is quadratic.

Q: What is the inverse operation of addition?

A: The inverse operation of addition is subtraction. In other words, if you add a number to another number, you can subtract that number to get back to the original number.

Q: What is the inverse operation of multiplication?

A: The inverse operation of multiplication is division. In other words, if you multiply a number by another number, you can divide that number to get back to the original number.

Q: How do I simplify an equation?

A: To simplify an equation, you need to combine like terms and cancel out coefficients. For example, if you have the equation 2x + 3x = 5x, you can combine the like terms to get 5x = 5x.

Q: What is a coefficient?

A: A coefficient is a number that is multiplied by a variable. For example, in the equation 2x = 4, the coefficient is 2.

Q: How do I check my solution?

A: To check your solution, you need to plug it back into the original equation and see if it is true. For example, if you solve the equation x + 2 = 0 and get x = -2, you can plug -2 back into the equation to see if it is true.

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 isolate the variable
  • Adding or subtracting constants to only one side of the equation
  • Not simplifying the equation
  • Not checking the solution

Conclusion

Solving linear equations is a fundamental skill that has many real-world applications. By following the steps outlined in this article and practicing with different types of equations, you can become proficient in solving linear equations. Remember to always isolate the variable, add or subtract constants to both sides, and simplify the equation to find the solution.

Tips and Tricks

  • Always read the equation carefully and identify the variable and constant terms.
  • Use inverse operations to isolate the variable, such as adding or subtracting constants to both sides.
  • Simplify the equation by combining like terms and canceling out coefficients.
  • Check your solution by plugging it back into the original equation.

Real-World Applications

Solving linear equations has many real-world applications, such as:

  • Calculating the cost of goods and services
  • Determining the amount of time it takes to complete a task
  • Finding the area and perimeter of shapes
  • Solving problems in physics, engineering, and other fields

Common Mistakes to Avoid

  • Failing to isolate the variable
  • Adding or subtracting constants to only one side of the equation
  • Not simplifying the equation
  • Not checking the solution