Solve For $w$. − 5 2 W + 7 2 = − 2 3 W − 7 -\frac{5}{2}w + \frac{7}{2} = -\frac{2}{3}w - 7 − 2 5 W + 2 7 = − 3 2 W − 7 Simplify Your Answer As Much As Possible. W = W = W =
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 type of linear equation, which involves isolating the variable w. We will use a step-by-step approach to simplify the equation and find the value of w.
The Given Equation
The given equation is:
Our goal is to isolate the variable w and simplify the equation as much as possible.
Step 1: Multiply Both Sides by the Least Common Multiple (LCM)
To eliminate the fractions, we need to multiply both sides of the equation by the least common multiple (LCM) of the denominators. In this case, the LCM is 6.
Multiplying both sides by 6:
$6 \times \left(-\frac{5}{2}w + \frac{7}{2}\right) = 6 \times \left(-\frac{2}{3}w - 7\right)$
This simplifies to:
Step 2: Add 15w to Both Sides
To isolate the term with w, we need to add 15w to both sides of the equation.
Adding 15w to both sides:
$-15w + 15w + 21 = -4w + 15w - 42$
This simplifies to:
Step 3: Add 42 to Both Sides
To further isolate the term with w, we need to add 42 to both sides of the equation.
Adding 42 to both sides:
$21 + 42 = 11w - 42 + 42$
This simplifies to:
Step 4: Divide Both Sides by 11
Finally, to find the value of w, we need to divide both sides of the equation by 11.
Dividing both sides by 11:
$\frac{63}{11} = \frac{11w}{11}$
This simplifies to:
Simplifying the Answer
We can simplify the answer by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3.
Simplifying the answer:
$w = \frac{21}{11}$
Conclusion
In this article, we solved a linear equation involving the variable w. We used a step-by-step approach to simplify the equation and find the value of w. By following these steps, we were able to isolate the variable w and simplify the equation as much as possible.
Final Answer
The final answer is:
w = \frac{21}{11}$<br/>
**Solving Linear Equations: A Q&A Guide**
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In our previous article, we solved a linear equation involving the variable w. We used a step-by-step approach to simplify the equation and find the value of w. In this article, we will provide a Q&A guide to help you understand the concept of solving linear equations and how to apply it to different types of equations. 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 ax + b = c, where a, b, and c are constants. A: The first step in solving a linear equation is to simplify the equation by combining like terms. This involves adding or subtracting the same term to both sides of the equation. A: To eliminate fractions in a linear equation, you need to multiply both sides of the equation by the least common multiple (LCM) of the denominators. This will eliminate the fractions and make it easier to solve the equation. A: The least common multiple (LCM) is the smallest multiple that is common to two or more numbers. For example, the LCM of 2 and 3 is 6. A: To add or subtract fractions in a linear equation, you need to have the same denominator. If the denominators are different, you need to find the least common multiple (LCM) and multiply both sides of the equation by the LCM. A: The order of operations in solving a linear equation is: A: To check your answer in a linear equation, you need to substitute the value of the variable back into the original equation and simplify. If the equation is true, then your answer is correct. A: Some common mistakes to avoid when solving linear equations include: In this article, we provided a Q&A guide to help you understand the concept of solving linear equations and how to apply it to different types of equations. By following the steps outlined in this article, you will be able to solve linear equations with confidence and accuracy. Here are some common linear equations that you may encounter: Here are some practice problems to help you apply the concepts learned in this article: Here are the answers to the practice problems:Introduction
Q: What is a linear equation?
Q: What is the first step in solving a linear equation?
Q: How do I eliminate fractions in a linear equation?
Q: What is the least common multiple (LCM)?
Q: How do I add or subtract fractions in a linear equation?
Q: What is the order of operations in solving a linear equation?
Q: How do I check my answer in a linear equation?
Q: What are some common mistakes to avoid when solving linear equations?
Conclusion
Final Tips
Common Linear Equations
Practice Problems
Answer Key