Question

What is the value of v?



45(v−7)=2



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

Answer 1

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:
\[
\boxed{7 \frac{2}{45}}
\]