The equation you've written seems to follow a specific format or notation that might imply ratios or proportions, such as:

\[
\frac{t - 42.8}{7.3} = \frac{t}{0.1}
\]

If this is the intended form, we can solve it step by step.

### Step 1: Write out the equation

\[
\frac{t - 42.8}{7.3} = \frac{t}{0.1}
\]

### Step 2: Cross-multiply

Multiply both sides to eliminate the fractions:

\[
(t - 42.8) \cdot 0.1 = t \cdot 7.3
\]

### Step 3: Expand both sides

\[
0.1t - 4.28 = 7.3t
\]

### Step 4: Bring all terms involving \(t\) to one side

\[
0.1t - 7.3t = 4.28
\]

### Step 5: Combine like terms

\[
-7.2t = 4.28
\]

### Step 6: Solve for \(t\)

\[
t = \frac{4.28}{-7.2}
\]

Now, let's calculate the value of \(t\):

\[
t \approx -0.594
\]

### Final Answer:
\( t \approx -0.594 \)

Would you like further details or have any questions? 

Here are some related questions:
1. How do you solve similar proportional equations?
2. How does cross-multiplying work in equations?
3. What are the steps to solving linear equations involving fractions?
4. How do you check your solution after solving an equation?
5. Can you apply these steps to more complex ratios?

**Tip:** Always simplify fractions before cross-multiplying to avoid calculation errors.

Learn how to solve a proportional equation using cross-multiplication. This example solves for 't' in the equation t:42.8=7.3:0.1. Follow detailed steps to understand the concepts of proportions and linear equations. Suitable for students in Grades 8-10.

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