How many solutions does this equation have? $$ 3(3 t+13)=9 t $$

Question

UpStudy AI · Accepted Answer

To determine how many solutions the equation

$$
3(3t + 13) = 9t
$$

has, let's solve for $$ t $$ step by step.

1. **Expand the Left Side:**

Multiply the terms inside the parentheses by 3:

$$
   3 \times 3t + 3 \times 13 = 9t + 39
   $$

So, the equation becomes:

$$
   9t + 39 = 9t
   $$

2. **Subtract $$ 9t $$ from Both Sides:**

$$
   9t + 39 - 9t = 9t - 9t
   $$

Simplifying both sides:

$$
   39 = 0
   $$

3. **Analyze the Result:**

The statement $$ 39 = 0 $$ is a contradiction—it's never true. This means there's no value of $$ t $$ that can satisfy the original equation.

**Conclusion:**  
The equation

$$
3(3t + 13) = 9t
$$

has **no solutions**.
The equation has no solutions.

How many solutions does this equation have? \[ 3(3 t+13)=9 t \]