If 3(t+2)=t+5(2t+1),3(t+2)=t+5(2t+1), what is the value of t?

To solve the equation \( 3(t + 2) = t + 5(2t + 1) \) for \( t \), follow these steps:

### 1. **Expand both sides of the equation:**

On the left-hand side:
\[
3(t + 2) = 3t + 6
\]

On the right-hand side:
\[
5(2t + 1) = 10t + 5
\]

So the equation becomes:
\[
3t + 6 = t + 10t + 5
\]

### 2. **Combine like terms:**

Simplify the right-hand side by combining \( t \) and \( 10t \):
\[
3t + 6 = 11t + 5
\]

### 3. **Isolate \( t \):**

Subtract \( 3t \) from both sides:
\[
6 = 8t + 5
\]

Subtract 5 from both sides to further isolate the term with \( t \):
\[
1 = 8t
\]

### 4. **Solve for \( t \):**

Finally, divide both sides by 8:
\[
t = \frac{1}{8}
\]

So, the value of \( t \) is \( \boxed{\frac{1}{8}} \).

Would you like more details, or do you have any questions?

### Related Questions:
1. What is the solution for \( t \) if the equation is \( 4(t + 3) = t + 7(2t + 4) \)?
2. If \( t = \frac{1}{8} \), what is the value of \( 3t + 2 \)?
3. How would the solution change if the original equation was \( 3(t + 2) = t + 5(2t + 2) \)?
4. Solve for \( t \) in the equation \( 2(t - 4) = 3t + 10 \).
5. What is the value of \( t \) if \( 5(t + 1) = 2t + 8 \)?

**Tip:** Always start by simplifying both sides of an equation before solving for the variable.

Learn how to solve the linear equation 3(t + 2) = t + 5(2t + 1) with a step-by-step solution. This problem involves distributing terms, combining like terms, and isolating variables. Suitable for students in Grades 7-9.

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