https://file.aiquickdraw.com/mathbot/file/1726428724723ft7u87f7.jpg

The equation shown in the image is:

\[
(1 - y) \cdot 10 = (y + 1) \cdot 2
\]

Let’s solve it step by step:

1. **Expand both sides**:
   - Left-hand side: \((1 - y) \cdot 10 = 10 - 10y\)
   - Right-hand side: \((y + 1) \cdot 2 = 2y + 2\)

   This gives us:

   \[
   10 - 10y = 2y + 2
   \]

2. **Move all terms involving \(y\) to one side** and the constants to the other:

   \[
   10 - 2 = 2y + 10y
   \]
   
   Simplifying:

   \[
   8 = 12y
   \]

3. **Solve for \(y\)**:

   \[
   y = \frac{8}{12} = \frac{2}{3}
   \]

So, the solution is:

\[
y = \frac{2}{3}
\]

Would you like more details or further clarification? Here are some related questions to extend this:

1. What happens if we change the equation to \((1 + y) \cdot 10 = (y - 1) \cdot 2\)?
2. How do we solve the same equation if it involves fractions?
3. What is the general approach for solving equations with variables on both sides?
4. How can we check if the solution \(y = \frac{2}{3}\) is correct?
5. What is the importance of distributing constants in algebraic expressions?

**Tip**: Always simplify both sides of the equation first before moving terms around to solve for the unknown.

Learn how to solve the linear equation (1 - y) * 10 = (y + 1) * 2 with a step-by-step guide. This problem involves algebraic concepts like the distributive property and solving for variables, making it suitable for 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