Questions: Solve for V. -7/2 v - 2/5 = 7 v + 4/5 Simplify your answer as much as possible. v=

Transcript text: Solve for $V$. \[ -\frac{7}{2} v-\frac{2}{5}=7 v+\frac{4}{5} \] Simplify your answer as much as possible. \[ v= \]

Solution

Solution Steps

Step 1: Rewrite the Equation

Start with the original equation: \[ -\frac{7}{2} v - \frac{2}{5} = 7 v + \frac{4}{5} \]

Step 2: Eliminate Fractions

To eliminate the fractions, find a common denominator, which is 10. Multiply every term by 10: \[ 10 \left(-\frac{7}{2} v\right) - 10 \left(\frac{2}{5}\right) = 10 \left(7 v\right) + 10 \left(\frac{4}{5}\right) \] This simplifies to: \[ -35 v - 4 = 70 v + 8 \]

Step 3: Combine Like Terms

Rearranging the equation to isolate $ v $: \[ -35 v - 70 v = 8 + 4 \] This simplifies to: \[ -105 v = 12 \]

Step 4: Solve for $ v $

Now, divide both sides by -105: \[ v = -\frac{12}{105} \] This can be simplified to: \[ v = -\frac{4}{35} \]