Solve The Equation For { X $} : : : { -2x - 10x + 12 = 18 \}

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will focus on solving a specific linear equation, step by step, to help you understand the process and build your confidence in solving similar equations.

The Equation

The equation we will be solving is:

$$-2x - 10x + 12 = 18$$

Step 1: Combine Like Terms

The first step in solving this equation is to combine like terms. In this case, we have two terms with the variable $x$, which are $-2x$ and $-10x$. We can combine these terms by adding their coefficients.

$$-2x - 10x = -12x$$

So, the equation becomes:

$$-12x + 12 = 18$$

Step 2: Isolate the Variable

The next step is to isolate the variable $x$. To do this, we need to get rid of the constant term on the left-hand side of the equation. We can do this by subtracting 12 from both sides of the equation.

$$-12x = 18 - 12$$

$$-12x = 6$$

Step 3: Solve for $x$

Now that we have isolated the variable $x$, we can solve for its value. To do this, we need to get rid of the coefficient of $x$, which is -12. We can do this by dividing both sides of the equation by -12.

$$x = \frac{6}{-12}$$

$$x = -\frac{1}{2}$$

Conclusion

In this article, we solved a linear equation step by step. We combined like terms, isolated the variable, and solved for its value. By following these steps, you can solve similar equations and build your confidence in mathematics.

Tips and Tricks

• Always combine like terms before isolating the variable.
• Use inverse operations to isolate the variable.
• Check your answer by plugging it back into the original equation.

Real-World Applications

Linear equations have many real-world applications, including:

• Physics: To describe the motion of objects.
• Engineering: To design and optimize systems.
• Economics: To model economic systems and make predictions.

Common Mistakes

• Not combining like terms before isolating the variable.
• Not using inverse operations to isolate the variable.
• Not checking the answer by plugging it back into the original equation.

Practice Problems

Try solving the following linear equations:

1. $2x + 5 = 11$
2. $-3x - 2 = 7$
3. $x + 2 = 9$

Solutions

1. $x = \frac{6}{2} = 3$
2. $x = \frac{-9}{-3} = 3$
3. $x = 7 - 2 = 5$

Conclusion

Introduction

In our previous article, we solved a linear equation step by step. However, we know that practice makes perfect, and the best way to learn is by asking questions and getting answers. In this article, we will provide a Q&A guide to help you understand linear equations and solve them with confidence.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (usually x) is 1. It can be written in the form 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 follow these steps:

1. Combine like terms.
2. Isolate the variable.
3. Solve for the value of the variable.

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, 2x and 4x are like terms because they both have the variable x and the exponent 1.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the like terms. For example, 2x + 4x = 6x.

Q: What is the inverse operation?

A: The inverse operation is an operation that undoes another operation. For example, addition and subtraction are inverse operations, as are multiplication and division.

Q: How do I use inverse operations to solve a linear equation?

A: To use inverse operations to solve a linear equation, you need to apply the inverse operation to both sides of the equation. For example, if you have the equation 2x + 5 = 11, you can subtract 5 from both sides to get 2x = 6, and then divide both sides by 2 to 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 before isolating the variable.
• Not using inverse operations to isolate the variable.
• Not checking the answer by plugging it back into the original equation.

Q: How do I check my answer?

A: To check your answer, you need to plug it back into the original equation and see if it is true. For example, if you have the equation 2x + 5 = 11 and you solve for x to get x = 3, you can plug x = 3 back into the equation to get 2(3) + 5 = 11, which is true.

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

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

• Physics: To describe the motion of objects.
• Engineering: To design and optimize systems.
• Economics: To model economic systems and make predictions.

Q: How can I practice solving linear equations?

A: You can practice solving linear equations by working on problems and exercises, such as those found in math textbooks or online resources. You can also try solving linear equations in real-world contexts, such as calculating the cost of goods or determining the amount of time it takes to complete a task.

Conclusion

Solving linear equations is a crucial skill in mathematics. By following the steps outlined in this article and practicing regularly, you can become proficient in solving linear equations and apply them to real-world problems. Remember to combine like terms, isolate the variable, and solve for its value, and don't be afraid to ask questions and seek help when you need it.