Math Problem Statement

What is the solution set of the given equation? 4y - 6y + 9y = -2

Solution

The equation given in the image is:

4y6y+9y=24y - 6y + 9y = -2

Let's simplify the left-hand side of the equation:

(4y6y+9y)=(46+9)y=7y(4y - 6y + 9y) = (4 - 6 + 9)y = 7y

So, the equation becomes:

7y=27y = -2

To solve for yy, divide both sides by 7:

y=27y = \frac{-2}{7}

Thus, the solution set of the equation is:

y=27\boxed{y = -\frac{2}{7}}

Would you like more details on this solution? Here are five related questions:

  1. How would you verify the solution to a linear equation?
  2. What are the steps for simplifying expressions like 4y6y+9y4y - 6y + 9y?
  3. How does dividing both sides of an equation work when solving for a variable?
  4. What are some common mistakes to avoid when simplifying linear equations?
  5. Can you apply this method to solve more complex equations?

Tip: Always combine like terms first when solving algebraic equations to simplify the expression efficiently.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Simplifying Expressions

Formulas

Simplification of like terms
Solving for a variable in a linear equation

Theorems

Properties of Equality

Suitable Grade Level

Grades 6-8