Solve For $x$.$-22-\frac{x}{9}=-19$ Answer: $x = \square$

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 type of linear equation, which is in the form of $ax + b = c$. We will use a step-by-step approach to solve the equation $-22 - \frac{x}{9} = -19$.

What are Linear Equations?

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, and $x$ is the variable. Linear equations can be solved using various methods, including algebraic manipulation, graphing, and substitution.

The Equation to be Solved

The equation we will be solving is $-22 - \frac{x}{9} = -19$. This equation is a linear equation in one variable, and it can be solved using algebraic manipulation.

Step 1: Add $\frac{x}{9}$ to Both Sides

To solve the equation, we need to isolate the variable $x$. The first step is to add $\frac{x}{9}$ to both sides of the equation. This will eliminate the fraction and make it easier to solve for $x$.

-22 - x/9 = -19
-22 - x/9 + x/9 = -19 + x/9
-22 = -19 + x/9

Step 2: Add 22 to Both Sides

The next step is to add 22 to both sides of the equation. This will eliminate the negative term and make it easier to solve for $x$.

-22 = -19 + x/9
-22 + 22 = -19 + 22 + x/9
0 = 3 + x/9

Step 3: Subtract 3 from Both Sides

The next step is to subtract 3 from both sides of the equation. This will eliminate the constant term and make it easier to solve for $x$.

0 = 3 + x/9
0 - 3 = 3 - 3 + x/9
-3 = x/9

Step 4: Multiply Both Sides by 9

The final step is to multiply both sides of the equation by 9. This will eliminate the fraction and give us the value of $x$.

-3 = x/9
-3 * 9 = x/9 * 9
-27 = x

Conclusion

In this article, we solved the linear equation $-22 - \frac{x}{9} = -19$ using a step-by-step approach. We added $\frac{x}{9}$ to both sides, added 22 to both sides, subtracted 3 from both sides, and finally multiplied both sides by 9 to get the value of $x$. The final answer is $x = -27$.

Tips and Tricks

• When solving linear equations, it's essential to follow the order of operations (PEMDAS) to ensure that you're performing the operations in the correct order.
• When adding or subtracting fractions, make sure to find a common denominator to avoid errors.
• When multiplying or dividing fractions, make sure to multiply or divide the numerators and denominators separately.

Common Mistakes to Avoid

• Not following the order of operations (PEMDAS) can lead to errors in solving linear equations.
• Not finding a common denominator when adding or subtracting fractions can lead to errors.
• Not multiplying or dividing fractions correctly can lead to errors.

Real-World Applications

Linear equations have numerous real-world applications, including:

• 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.

Conclusion

Introduction

In our previous article, we discussed how to solve linear equations using a step-by-step approach. In this article, we will provide a Q&A guide to help students understand the concepts and techniques involved in 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 of $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Q: What are the steps to solve a linear equation?

A: The steps to solve a linear equation are:

1. Add or subtract the same value to both sides of the equation to isolate the variable.
2. Multiply or divide both sides of the equation by the same value to eliminate the fraction.
3. Simplify the equation to get the value of the variable.

Q: How do I add or subtract fractions in a linear equation?

A: To add or subtract fractions in a linear equation, you need to find a common denominator. The common denominator is the least common multiple (LCM) of the denominators of the fractions. Once you have found the common denominator, you can add or subtract the fractions.

Q: How do I multiply or divide fractions in a linear equation?

A: To multiply or divide fractions in a linear equation, you need to multiply or divide the numerators and denominators separately. For example, if you have the equation $\frac{x}{3} \times \frac{2}{5}$, you would multiply the numerators and denominators separately to get $\frac{2x}{15}$.

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

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

• Not following the order of operations (PEMDAS)
• Not finding a common denominator when adding or subtracting fractions
• Not multiplying or dividing fractions correctly
• Not simplifying the equation to get the value of the variable

Q: How do I check my answer when solving a linear equation?

A: To check your answer when solving a linear equation, you can plug the value of the variable back into the original equation and see if it is true. If the equation is true, then your answer is correct.

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

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

• 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.

Q: How can I practice solving linear equations?

A: You can practice solving linear equations by working through examples and exercises in a textbook or online resource. You can also try solving linear equations on your own using a calculator or computer program.

Conclusion

In conclusion, solving linear equations is a crucial skill for students to master. By following a step-by-step approach and avoiding common mistakes, students can solve linear equations with ease. The real-world applications of linear equations are numerous, and understanding how to solve them is essential for success in various fields.

Additional Resources

• Khan Academy: Linear Equations
• Mathway: Linear Equations
• Wolfram Alpha: Linear Equations

Final Tips

• Practice solving linear equations regularly to build your skills and confidence.
• Use a calculator or computer program to check your answers and get feedback.
• Don't be afraid to ask for help if you're struggling with a particular concept or technique.