To solve the given equation, we need to simplify both sides of the equation and isolate the variable, 't'. Let's solve it step by step.



We have: 3t - 2/4 - 2t 3/3

First, let's simplify the fractions:
- 2/4 = 1/2 (by dividing the numerator and denominator by 2)
- 3/3 = 1 (since any number divided by itself is always 1)

Now, let's rewrite the equation:

3t - 1/2 - 2t + 1

Next, let's combine the like terms (terms with the same variable):

(3t - 2t) - 1/2 + 1

Simplifying further:

t - 1/2 + 1



The right side of the equation is 2/3 - t. We don't need to simplify it further.



Now, let's rewrite the equation using the simplified expressions from the previous steps:

t - 1/2 + 1 = 2/3 - t



To isolate the variable 't', let's get rid of the fractions first. We can do this by multiplying both sides of the equation by the least common denominator (LCD), which is 6.

6(t - 1/2 + 1) = 6(2/3 - t)

Simplifying both sides:

6t - 3 + 6 = 4 - 6t

Combine like terms again:

6t - 3 + 6 = 4 - 6t

6t + 3 = 4 - 6t

Next, let's get rid of the variable on one side of the equation. We can do this by adding 6t to both sides:

6t + 3 + 6t = 4 - 6t + 6t

Simplifying both sides:

12t + 3 = 4

Finally, let's isolate the variable by subtracting 3 from both sides:

12t + 3 - 3 = 4 - 3

Simplifying both sides:

12t = 1

Now, to find the value of 't', we divide both sides by 12:

12t/12 = 1/12

Simplifying:

t = 1/12

Therefore, the solution to the given equation is t = 1/12.