https://file.aiquickdraw.com/mathbot/file/17254137688618oj0je5k.jpg

The problem presents the equation \(\frac{w}{2} - 21 = -15\) and requires selecting the reasons for each step in the solution process.

### Steps in the Solution:

1. **Given Equation**: \(\frac{w}{2} - 21 = -15\)
   - **Reason**: This is the original equation provided.

2. **Step**: \(\frac{w}{2} - 21 + 21 = -15 + 21\)
   - **Reason**: **Addition Property of Equality**. Here, 21 is added to both sides to isolate the term with \(w\).

3. **Step**: \(\frac{w}{2} = 6\)
   - **Reason**: **Simplification**. After adding 21 to both sides, the equation simplifies to \(\frac{w}{2} = 6\).

4. **Step**: \(w = 2 \times 6\)
   - **Reason**: **Multiplication Property of Equality**. To solve for \(w\), both sides are multiplied by 2.

5. **Step**: \(w = 12\)
   - **Reason**: **Simplification**. This is the final simplified solution for \(w\).

Would you like more details on any of the steps, or do you have any other questions?

### Related Questions:
1. What is the Addition Property of Equality?
2. How does the Multiplication Property of Equality work?
3. Why is it important to perform the same operation on both sides of an equation?
4. How would you check if \(w = 12\) is the correct solution to the original equation?
5. What other methods can be used to solve linear equations?

**Tip:** Always verify your solution by substituting it back into the original equation to ensure it satisfies the equation.

The equation \(\frac{w}{2} - 21 = -15\) is solved in several steps. For each step, choose the reason that best justifies it.

Learn how to solve the linear equation \(\frac{w}{2} - 21 = -15\) step-by-step and understand the mathematical reasoning behind each step. This guide covers algebraic concepts such as the Addition and Multiplication Properties of Equality, suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation