To solve the equation \(2x + 3x + 56x = 4566y + 4546x\), we first combine like terms on the left-hand side:

\[2x + 3x + 56x = (2 + 3 + 56)x = 61x\]

So the equation simplifies to:

\[61x = 4566y + 4546x\]

Next, we isolate \(x\) on one side of the equation:

\[61x - 4546x = 4566y\]

This simplifies to:

\[-4485x = 4566y\]

We can divide both sides by -4485 to solve for \(x\):

\[x = -\frac{4566y}{4485}\]

To simplify further, we find the greatest common divisor (GCD) of 4566 and 4485 and divide both the numerator and denominator by the GCD:

\[\text{GCD}(4566, 4485) = 3\]

So:

\[x = -\frac{4566 \div 3}{4485 \div 3} = -\frac{1522}{1495}\]

Thus, the solution is:

\[x = -\frac{1522}{1495}y\]

Do you want more details or have any questions? Here are some questions you might want to explore next:

1. How to find the GCD of two numbers?
2. What are the properties of linear equations?
3. How to isolate variables in an equation?
4. How to simplify fractions?
5. What are the common methods for solving algebraic equations?

**Tip:** When simplifying fractions, always look for the greatest common divisor (GCD) to reduce the fraction to its simplest form.

Learn how to solve the equation 2x + 3x + 56x = 4566y + 4546x step-by-step. This problem covers algebraic concepts such as combining like terms, isolating variables, and simplifying fractions using the greatest common divisor (GCD). Suitable for students in Grades 10-12.

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