Math Problem Statement

Solve for y: 9y - y = 16

Solution

The equation provided is:

9yy=169y - y = 16

To solve for yy:

  1. Combine like terms on the left-hand side of the equation: (9yy)=8y(9y - y) = 8y

    So, the equation simplifies to: 8y=168y = 16

  2. To solve for yy, divide both sides of the equation by 8: y=168y = \frac{16}{8}

  3. Simplify the right-hand side: y=2y = 2

So, the solution is y=2y = 2.

Would you like more details on any part of this solution, or do you have any other questions?


Here are some related questions for further exploration:

  1. What would be the solution if the equation was 9y2y=189y - 2y = 18?
  2. How would the solution change if the equation was 9yy=109y - y = 10 instead?
  3. What steps would you take if the equation had a constant on the left side, like 9yy+3=169y - y + 3 = 16?
  4. Can you solve for yy if the equation was 9yy=09y - y = 0?
  5. What happens if yy is a fraction, say 9yy=129y - y = \frac{1}{2}?

Tip: Always combine like terms first when solving linear equations to simplify the equation before solving for the variable.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Combining like terms
Solving linear equations

Theorems

Basic arithmetic principles

Suitable Grade Level

Grades 6-8