Solve the equation and check your solution. Thank You
3/v= v/2v+9
I will help you. What gradelevel?
I am sure you meant
3/v= v/(2v+9)
if so, then
v^2 = 6v + 27
v^2 - 6v - 27 = 0
(v-9)(v+3) = 0
v = 9 or v = -3
v^2 = 6v + 27
v^2 - 6v - 27 = 0
(v-9)(v+3) = 0
v = 9 or v = -3
v would equal 9
To solve the equation 3/v = v/2v + 9, we can start by simplifying both sides of the equation.
On the left side, we have 3/v. We can rewrite this as 3 * (1/v) or 3v^(-1).
On the right side, we have v/2v + 9. We can simplify this as 1/2 + 9, which becomes 1/2 + 18/2. Combining the fractions, we get 19/2.
Now, our equation becomes 3v^(-1) = 19/2.
To solve for v, we can multiply both sides of the equation by v to remove the denominator:
3v^(-1) * v = (19/2) * v
On the left side, v^(-1) * v is equal to 1, so we are left with just 3v:
3v = (19/2) * v
Next, we want to isolate v. We can start by subtracting (19/2) * v from both sides of the equation:
3v - (19/2) * v = 0
Combining like terms on the left side, we have:
(3 - 19/2) * v = 0
To simplify further, we need to find a common denominator for 3 and 19/2. The common denominator is 2, so we have:
(6/2 - 19/2) * v = 0
(-13/2) * v = 0
Now, we have (-13/2) * v = 0. To solve for v, we can divide both sides of the equation by (-13/2):
v = 0 / (-13/2)
When we divide 0 by any number, the result is always 0. Therefore, v = 0.
To check our solution, we can substitute v = 0 back into the original equation:
3/v = v/2v + 9
Substituting v = 0, we have:
3/0 = 0/2(0) + 9
Since division by 0 is undefined, the left side of the equation is undefined.
Therefore, there is no solution to the equation 3/v = v/2v + 9.