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What is the value of v?



45(v−7)=2



Enter your answer as a mixed number in simplest form in the box.

1 answer

To solve the equation \( 45(v - 7) = 2 \), we start by isolating the expression containing \( v \).

  1. Divide both sides by 45: \[ v - 7 = \frac{2}{45} \]

  2. Next, add 7 to both sides to solve for \( v \): \[ v = \frac{2}{45} + 7 \]

  3. To combine these terms, express 7 as a fraction: \[ 7 = \frac{7 \times 45}{45} = \frac{315}{45} \] Thus, we can rewrite \( v \): \[ v = \frac{2}{45} + \frac{315}{45} \]

  4. Now, add the fractions: \[ v = \frac{2 + 315}{45} = \frac{317}{45} \]

  5. The fraction \( \frac{317}{45} \) can be converted into a mixed number. First, divide 317 by 45: \[ 317 \div 45 = 7 \quad \text{(since } 45 \times 7 = 315\text{)} \] The remainder is: \[ 317 - 315 = 2 \]

  6. Therefore, we express \( \frac{317}{45} \) as a mixed number: \[ v = 7 \frac{2}{45} \]

Thus, the final answer is: \[ \boxed{7 \frac{2}{45}} \]