Questions: Solve for (v). [ 25=-frac52 v ] Simplify your answer as much as possible. [ v= ]

$Solve for (v). [ 25=-frac52 v ] Simplify your answer as much as possible. [ v= ]$

Transcript text: Solve for $v$. \[ 25=-\frac{5}{2} v \] Simplify your answer as much as possible. \[ v= \]

Solution

Solution Steps

To solve for $ v $ in the equation $ 25 = -\frac{5}{2} v $, we need to isolate $ v $. This can be done by multiplying both sides of the equation by the reciprocal of $-\frac{5}{2}$, which is $-\frac{2}{5}$. This will cancel out the coefficient of $ v $ on the right side, leaving $ v $ by itself.

Step 1: Set Up the Equation

We start with the equation: \[ 25 = -\frac{5}{2} v \]

Step 2: Isolate $ v $

To isolate $ v $, we multiply both sides by the reciprocal of $-\frac{5}{2}$: \[ v = 25 \cdot \left(-\frac{2}{5}\right) \]

Step 3: Perform the Calculation

Calculating the right-hand side: \[ v = 25 \cdot -0.4 = -10.0 \]