Solve: `((t-7))/5=((8-5t))/9`

Answer

To solve the equation \(\frac{t-7}{5} = \frac{8-5t}{9}\), we will follow these steps:

### Step 1: Cross-Multiply
To eliminate the fractions, we can cross-multiply. This means we will multiply the numerator of one side by the denominator of the other side.

\[ 9(t - 7) = 5(8 - 5t) \]

### Step 2: Distribute
Now, we will distribute on both sides of the equation.

\[ 9t - 63 = 40 - 25t \]

### Step 3: Move the Terms Involving \(t\) to One Side
Next, we will move all terms involving \(t\) to one side and constant terms to the other side. We can add \(25t\) to both sides and add \(63\) to both sides.

\[ 9t + 25t = 40 + 63 \]

### Step 4: Combine Like Terms
Now we will combine the like terms on both sides.

\[ 34t = 103 \]

### Step 5: Solve for \(t\)
Finally, we will solve for \(t\) by dividing both sides by \(34\).

\[ t = \frac{103}{34} \]

### Final Answer
Thus, the solution to the equation is:

\[ t = \frac{103}{34} \]

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