Solve The Equation To Find W W W . 2 W − 8 = − 24 2w - 8 = -24 2 W − 8 = − 24 ${ \begin{aligned} 2w - 8 + 8 & = -24 + 8 \ 2w & = -16 \ w & = ? \end{aligned} }$

Mar 13, 2025 by ADMIN 161 views

**Solving Linear Equations: A Step-by-Step Guide**

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 to find the value of $w$ . The equation is $2w - 8 = -24$ , and we will use algebraic techniques to isolate the variable $w$ .

Understanding the Equation

The given equation is a linear equation in one variable, $w$ . The equation is in the form of $ax + b = c$ , where $a$ , $b$ , and $c$ are constants. In this case, $a = 2$ , $b = -8$ , and $c = -24$ . Our goal is to solve for $w$ by isolating it on one side of the equation.

Step 1: Add 8 to Both Sides

To start solving the equation, we need to get rid of the constant term on the left-hand side. We can do this by adding 8 to both sides of the equation. This will keep the equation balanced and allow us to isolate the variable $w$ .

2w - 8 + 8 = -24 + 8

By adding 8 to both sides, we get:

2w = -16

Step 2: Divide Both Sides by 2

Now that we have isolated the variable $w$ on the left-hand side, we need to get rid of the coefficient 2. We can do this by dividing both sides of the equation by 2. This will give us the value of $w$ .

2w / 2 = -16 / 2

By dividing both sides by 2, we get:

w = -8

Conclusion

In this article, we solved a linear equation to find the value of $w$ . We started by adding 8 to both sides of the equation to get rid of the constant term. Then, we divided both sides by 2 to isolate the variable $w$ . The final answer is $w = -8$ .

Real-World Applications

Solving linear equations is a crucial skill in many 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.

Tips and Tricks

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

Use inverse operations: To isolate a variable, use inverse operations, such as addition and subtraction, multiplication and division.
Check your work: Always check your work by plugging the solution back into the original equation.
Use algebraic techniques: Use algebraic techniques, such as factoring and simplifying, to make the equation easier to solve.

Common Mistakes

Here are some common mistakes to avoid when solving linear equations:

Not checking your work: Failing to check your work can lead to incorrect solutions.
Not using inverse operations: Failing to use inverse operations can make the equation harder to solve.
Not simplifying the equation: Failing to simplify the equation can make it harder to solve.

Conclusion

Introduction

In our previous article, we discussed how to solve linear equations using algebraic techniques. 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. It is typically 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 on one side of the equation. You can do this by using inverse operations, such as addition and subtraction, multiplication and division.

Q: What are inverse operations?

A: Inverse operations are operations that "undo" each other. 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 identify the operation that is being performed on the variable. Then, you need to perform the inverse operation to isolate the variable.

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:

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

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

A: To check your work when solving a linear equation, you need to plug the solution back into the original equation and make sure it is true. If the solution is not true, then you need to go back and recheck your work.

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

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

Not checking your work
Not using inverse operations
Not simplifying the equation
Not following the order of operations

Q: How do I simplify a linear equation?

A: To simplify a linear equation, you need to combine like terms and eliminate any unnecessary operations.

Q: What is a like term?

A: A like term is a term that has the same variable and coefficient. For example, 2x and 4x are like terms.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the like terms.

Q: What is a coefficient?

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

Q: How do I eliminate unnecessary operations?

A: To eliminate unnecessary operations, you need to simplify the equation by combining like terms and eliminating any unnecessary operations.

Conclusion

Solving linear equations is a crucial skill in mathematics, and it has many real-world applications. By following the steps outlined in this article, you can solve linear equations with ease. Remember to use inverse operations, check your work, and simplify the equation to get the correct solution.

Additional Resources

If you are struggling to solve linear equations, there are many additional resources available to help you. Some of these resources include:

Online tutorials and videos
Math textbooks and workbooks
Online math communities and forums
Math tutors and instructors