If `(7t + 13)/(15) + 7 ((2t -1)/(5)) = 6`, then the value of t is _____

Options

A. 2
B. 3
C. 1
D. `-2`

Explanation

To solve the equation \(\frac{7t + 13}{15} + 7 \left(\frac{2t - 1}{5}\right) = 6\), we will follow these steps:

### Step 1: Simplify the equation
Start by rewriting the equation:
\[ \frac{7t + 13}{15} + 7 \cdot \frac{2t - 1}{5} = 6 \]

### Step 2: Simplify the second term
Multiply \(7\) with \(\frac{2t - 1}{5}\):
\[ 7 \cdot \frac{2t - 1}{5} = \frac{7(2t - 1)}{5} = \frac{14t - 7}{5} \]

### Step 3: Rewrite the equation
Now substitute this back into the equation:
\[ \frac{7t + 13}{15} + \frac{14t - 7}{5} = 6 \]

### Step 4: Find a common denominator
The common denominator for \(15\) and \(5\) is \(15\). Rewrite the second term:
\[ \frac{14t - 7}{5} = \frac{3(14t - 7)}{15} = \frac{42t - 21}{15} \]

### Step 5: Combine the fractions
Now combine the two fractions:
\[ \frac{7t + 13 + 42t - 21}{15} = 6 \]
This simplifies to:
\[ \frac{49t - 8}{15} = 6 \]

### Step 6: Eliminate the fraction
Multiply both sides by \(15\) to eliminate the fraction:
\[ 49t - 8 = 90 \]

### Step 7: Solve for \(t\)
Add \(8\) to both sides:
\[ 49t = 90 + 8 \]
\[ 49t = 98 \]
Now, divide both sides by \(49\):
\[ t = \frac{98}{49} = 2 \]

### Final Answer
The value of \(t\) is \(2\).

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