Solve for v.
v+6/5=3/5v-7/3
Simplify your answer as much as possible.
multiply each term by 15v, the LCD
15v^2 + 18v = 9 - 35v
15v^2 + 53v - 9 = 0
by the formula
v = (-53 ± √3349)/30
To solve for v in the equation v + 6/5 = 3/5v - 7/3, we'll first gather all terms with v on one side and all constant terms on the other side.
Step 1: First, let's isolate the terms with v on one side of the equation.
v + 6/5 = 3/5v - 7/3
Let's move the 3/5v term to the left side by subtracting it from both sides:
v + 6/5 - 3/5v = 3/5v - 7/3 - 3/5v
Simplifying both sides:
v - 3/5v + 6/5 = -7/3 - 3/5v
Step 2: Combine like terms on both sides of the equation:
(1 - 3/5)v + 6/5 = (-7/3 - 3/5)v
(2/5)v + 6/5 = (-35/15 - 9/15)v
(2/5)v + 6/5 = (-44/15)v
Step 3: Now, let's isolate v by moving the terms without v to the right side of the equation:
(2/5)v + (44/15)v = -6/5
Multiplying each term by the least common denominator (15) to clear the fractions:
3(2/5)v + 3(44/15)v = -6/5(15)
6v/5 + 44v/15 = -18/5
Step 4: Combine like terms:
(18v + 44v)/15 = -18/5
62v/15 = -18/5
Step 5: Cross-multiply:
(62v)(5) = (18)(15)
310v = 270
Step 6: Solve for v by dividing both sides by 310:
v = 270/310
Simplifying the fraction:
v = 27/31
So, the solution to the equation v + 6/5 = 3/5v - 7/3 is v = 27/31.