Question

Solve each equation. v+(2)/(3)+(3)/(2)v=-(7)/(2)

Answer 1

To solve the equation v+(2)/(3)+(3)/(2)v=-(7)/(2), you need to combine like terms and isolate the variable v on one side of the equation. The solution to the equation is v = -1.1053.

Step-by-step explanation:

To solve the equation v+(2)/(3)+(3)/(2)v=-(7)/(2), we need to combine like terms and isolate the variable v on one side of the equation. Here's how you can solve it:

1. Distribute the v to the terms inside the parentheses: v + (2/3)v + (3/2)v = -(7/2)
2. Combine the v terms by adding their coefficients: (1 + 2/3 + 3/2)v = -(7/2)
3. Add the fractions within the parentheses: (1 + 2/3 + 9/6)v = -(7/2)
4. Convert the mixed numbers to improper fractions: (1 + 2/3 + 3/2)v = -(7/2)
5. Combine the fractions: (6/6 + 4/6 + 9/6)v = -(7/2)
6. Combine the numerators: (19/6)v = -(7/2)
7. Multiply both sides of the equation by the reciprocal of 19/6 to isolate v: v = -(7/2) * (6/19)
8. Multiply the numerators and the denominators: v = -(42/38) = -1.1053

Therefore, the solution to the equation is v = -1.1053.