List The Steps To Solve The Following Equation: $5x - 6 = 44$. Then Solve For $x$.

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 walk you through the steps to solve a linear equation, using the equation $5x - 6 = 44$ as an example. We will also provide a step-by-step solution for $x$.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable (in this case, $x$) is 1. It can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Step 1: Write Down the Equation

The first step in solving a linear equation is to write down the equation. In this case, the equation is $5x - 6 = 44$.

Step 2: Add or Subtract the Same Value to Both Sides

The next step is to add or subtract the same value to both sides of the equation to isolate the variable term. In this case, we can add 6 to both sides of the equation to get rid of the negative term.

5x - 6 + 6 = 44 + 6

This simplifies to:

5x = 50

Step 3: Divide Both Sides by the Coefficient of the Variable

The next step is to divide both sides of the equation by the coefficient of the variable (in this case, 5). This will give us the value of $x$.

\frac{5x}{5} = \frac{50}{5}

This simplifies to:

x = 10

Step 4: Check the Solution

The final step is to check the solution by plugging it back into the original equation. If the equation holds true, then our solution is correct.

5(10) - 6 = 44

This simplifies to:

50 - 6 = 44

Which is true.

Conclusion

Solving linear equations is a straightforward process that involves a series of steps. By following these steps, we can solve equations like $5x - 6 = 44$ and find the value of $x$. Remember to always check your solution by plugging it back into the original equation.

Common Mistakes to Avoid

When solving linear equations, there are several common mistakes to avoid. These include:

• Not following the order of operations: When solving an equation, it's essential to follow the order of operations (PEMDAS) to ensure that you're performing the calculations correctly.
• Not checking the solution: It's crucial to check your solution by plugging it back into the original equation to ensure that it's correct.
• Not simplifying the equation: Simplifying the equation can make it easier to solve and reduce the risk of errors.

Real-World Applications

Linear equations have numerous real-world applications, including:

• Physics and engineering: Linear equations are used to describe the motion of objects and the behavior of physical systems.
• Economics: Linear equations are used to model economic systems and make predictions about economic trends.
• Computer science: Linear equations are used in computer science to solve problems and make predictions.

Tips and Tricks

Here are some tips and tricks to help you solve linear equations:

• Use a calculator: If you're struggling to solve an equation, try using a calculator to check your work.
• Simplify the equation: Simplifying the equation can make it easier to solve and reduce the risk of errors.
• Check your solution: It's essential to check your solution by plugging it back into the original equation to ensure that it's correct.

Conclusion

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Frequently Asked Questions

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (in this case, $x$) is 1. It can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Q: How do I solve a linear equation?

A: To solve a linear equation, follow these steps:

1. Write down the equation.
2. Add or subtract the same value to both sides of the equation to isolate the variable term.
3. Divide both sides of the equation by the coefficient of the variable.
4. Check the solution by plugging it back into the original equation.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when solving an equation. The order of operations is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify an equation?

A: To simplify an equation, combine like terms and eliminate any unnecessary operations. For example, if you have the equation $2x + 3x = 5x + 2$, you can simplify it by combining the like terms: $5x = 5x + 2$.

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 (in this case, $x$) is 1. A quadratic equation, on the other hand, is an equation in which the highest power of the variable is 2. For example, the equation $x^2 + 4x + 4 = 0$ is a quadratic equation.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you can use the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. You can also try factoring the equation or using the method of substitution.

Q: What is the significance of linear equations in real-world applications?

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

• Physics and engineering: Linear equations are used to describe the motion of objects and the behavior of physical systems.
• Economics: Linear equations are used to model economic systems and make predictions about economic trends.
• Computer science: Linear equations are used in computer science to solve problems and make predictions.

Q: How do I check my solution to a linear equation?

A: To check your solution to a linear equation, plug the solution back into the original equation and verify that it is true. For example, if you have the equation $2x + 3 = 5$ and you solve for $x$, you can plug the solution back into the equation to verify that 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:

• Not following the order of operations: When solving an equation, it's essential to follow the order of operations (PEMDAS) to ensure that you're performing the calculations correctly.
• Not checking the solution: It's crucial to check your solution by plugging it back into the original equation to ensure that it's correct.
• Not simplifying the equation: Simplifying the equation can make it easier to solve and reduce the risk of errors.

Conclusion

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. By following the steps outlined in this article, you can solve linear equations and find the value of $x$. Remember to always check your solution by plugging it back into the original equation and to avoid common mistakes like not following the order of operations and not simplifying the equation.