Math Problem Statement

4y+3=2y+5 What is y?

Solution

To solve the equation 4y+3=2y+54y + 3 = 2y + 5, follow these steps:

  1. Subtract 2y2y from both sides of the equation to group the yy-terms on one side: 4y2y+3=54y - 2y + 3 = 5 This simplifies to: 2y+3=52y + 3 = 5

  2. Subtract 33 from both sides to isolate the 2y2y-term: 2y=532y = 5 - 3 Simplifying the right-hand side: 2y=22y = 2

  3. Divide both sides by 2 to solve for yy: y=22=1y = \frac{2}{2} = 1

Thus, y=1y = 1.

Would you like more details or have any questions?

Here are 5 related questions to further your understanding:

  1. How would you solve 3y+7=5y+13y + 7 = 5y + 1?
  2. What happens if 4y+3=2y+54y + 3 = 2y + 5 were an inequality instead of an equation?
  3. Can you solve 6y+9=3y+156y + 9 = 3y + 15?
  4. What is the difference between solving an equation and simplifying an expression?
  5. How can you check if your solution for yy is correct?

Tip: Always check your solution by plugging it back into the original equation to ensure both sides are equal.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Basic Linear Equation Manipulation

Theorems

Addition and Subtraction Properties of Equality
Division Property of Equality

Suitable Grade Level

Grades 6-8