How many solutions does this equation have?
7 - 10t = 5t - 8
no solution
one solution
infinitely many solutions

To determine the number of solutions for the equation \( 7 - 10t = 5t - 8 \), we can isolate \( t \) and analyze the result.

### Steps:
1. **Move all terms involving \( t \) to one side of the equation:**
   \[
   7 - 10t = 5t - 8
   \]
   Add \( 10t \) to both sides:
   \[
   7 = 15t - 8
   \]

2. **Move constant terms to the other side:**
   Add \( 8 \) to both sides:
   \[
   15 = 15t
   \]

3. **Solve for \( t \):**
   Divide both sides by \( 15 \):
   \[
   t = 1
   \]

Since we found a single unique value for \( t \), the equation has **one solution**.

### Answer:
- **One solution**

Would you like a more detailed explanation, or do you have any questions?

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1. How can you tell if an equation has no solutions?
2. What are the steps to check if an equation has infinitely many solutions?
3. How does isolating variables help in solving linear equations?
4. Can equations with different variables on each side still have solutions?
5. What is the significance of the solution in real-world applications?

**Tip:** Always check your solution by substituting it back into the original equation to verify.

How many solutions does this equation have? 7 - 10t = 5t - 8

Explore the solution to determine how many solutions exist for the equation 7 - 10t = 5t - 8. This problem covers essential algebraic techniques, including isolating variables and checking for single solutions. Suitable for students in Grades 7-9.

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