5t-3/-2=t+3/2

5t-(-3/2)=t+(3/2)

Subtract both sides by t.
4t+(3/2)=(3/2)
Subtract both sides by (3/2).
4t=0
Divide both sides by 4.
t=0

To solve the equation 5t - 3/-2 = t + 3/2, let's simplify both sides of the equation step by step.

Step 1: Distribute the negative sign to the terms in the numerator of the fraction on the left side:
5t + (3/-2) = t + 3/2

Step 2: Simplify the fraction on the left side:
5t - 3/2 = t + 3/2

Step 3: Subtract t from both sides to isolate the variable t:
5t - t - 3/2 = 3/2

Step 4: Combine like terms:
4t - 3/2 = 3/2

Step 5: Add 3/2 to both sides to eliminate the fraction on the left side:
4t - 3/2 + 3/2 = 3/2 + 3/2

Step 6: Combine the fractions on the left side:
4t - (3/2 - 3/2) = 3/2

Step 7: Simplify the fraction on the left side:
4t - 0 = 3/2

Step 8: Remove the 0 on the left side:
4t = 3/2

Step 9: Divide both sides by 4 to solve for t:
(4t)/4 = (3/2)/4

Step 10: Simplify the equation:
t = 3/8

Therefore, the solution to the equation 5t - 3/-2 = t + 3/2 is t = 3/8.