5y+105−710=−13y−1010

give me solution

Let's solve the equation step by step:

The given equation is:

\[
5y + 105 - 710 = -13y - 1010
\]

### Step 1: Simplify the equation
First, let's simplify both sides by combining like terms. We have constants and coefficients of \( y \).

\[
5y + (105 - 710) = -13y - 1010
\]

Simplify the constants:

\[
5y - 605 = -13y - 1010
\]

### Step 2: Move the terms involving \( y \) to one side
Add \( 13y \) to both sides to move the terms involving \( y \) to the left side:

\[
5y + 13y - 605 = -1010
\]

Combine like terms:

\[
18y - 605 = -1010
\]

### Step 3: Move the constant terms to the other side
Add \( 605 \) to both sides to move the constant term to the right side:

\[
18y = -1010 + 605
\]

Simplify the right side:

\[
18y = -405
\]

### Step 4: Solve for \( y \)
Divide both sides by 18 to solve for \( y \):

\[
y = \frac{-405}{18}
\]

Simplify the fraction:

\[
y = -22.5
\]

### Solution
The solution to the equation is \( y = -22.5 \).

Would you like more details or have any questions? Here are some related questions to explore:

1. How do you solve equations with variables on both sides?
2. What are the steps to isolate a variable in an equation?
3. How do you check if a solution to an equation is correct?
4. What are like terms in an algebraic equation?
5. How do you simplify fractions?
6. What is the importance of balancing an equation?
7. Can equations have more than one solution?
8. What happens if you have no solution or infinite solutions in an equation?

**Tip:** Always combine like terms before moving variables and constants to one side.

Learn how to solve the equation 5y + 105 - 710 = -13y - 1010 step-by-step with a detailed explanation. This problem involves simplifying equations with variables on both sides and is suitable for students in Grades 7-9.

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