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The image you provided shows an equation where you are asked to solve for \( t \). The equation appears to be:

\[
\frac{2}{3}t = \frac{3}{4} + \frac{t}{6} + \frac{4}{5}t
\]

Let's solve this equation step by step.

### Step 1: Eliminate the fractions
To eliminate the fractions, we can multiply every term by the least common denominator (LCD) of all the fractions. The denominators here are 3, 4, 6, and 5. The LCD of these numbers is 60.

Multiply every term by 60:

\[
60 \times \frac{2}{3}t = 60 \times \frac{3}{4} + 60 \times \frac{t}{6} + 60 \times \frac{4}{5}t
\]

This simplifies to:

\[
40t = 45 + 10t + 48t
\]

### Step 2: Combine like terms
Next, combine the terms that have \( t \) on both sides of the equation:

\[
40t - 10t - 48t = 45
\]

Simplify the equation:

\[
-18t = 45
\]

### Step 3: Solve for \( t \)
To solve for \( t \), divide both sides of the equation by \(-18\):

\[
t = \frac{45}{-18}
\]

Simplify the fraction:

\[
t = -\frac{5}{2} \text{ or } t = -2.5
\]

### Final Answer:
The value of \( t \) is \( t = -2.5 \).

Would you like more details or have any questions? Here are some related questions you might find useful:

1. What are some other methods to solve linear equations with fractions?
2. How do you find the least common denominator (LCD) for multiple fractions?
3. Can you explain how to combine like terms in an algebraic equation?
4. What happens when the equation has no solution?
5. How would you solve a similar equation if it were a quadratic instead of linear?

**Tip:** Always double-check your solutions by substituting them back into the original equation to ensure they satisfy the equation.

Learn how to solve the linear equation 2/3 t = 3/4 + t/6 + 4/5 t using step-by-step techniques including finding the least common denominator and combining like terms. Ideal for students in Grades 8-10.

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