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

I'm having a hard time to solve this problem >.<

cancel out the denominator by multiplying by greatest common factor so 2.

2(5/2t-t)=2(3+3/2t)
so now equation is 5t-2t=6+3t
then solve. 3t=6+3t
you should get no solution

I don't understand....

Anon failed to notice that t is also in the denominator.

Multiply both sides by 2t.

5 - 2t^2 = 6t + 3

Combine like terms.

2 - 2t^2 -6t = 0

Multiply by -1.

2t^2 + 6t - 2 = 0

I also get no solution, but at least my equation is correct.

Anon is correct.

3t=6+3t

When we subtract 3t from both sides of the equation, we no longer have an equation. 0 = t is meaningless; therefore this problem has no solution.

Don't worry, I'm here to help you solve the problem step by step. Let's start by simplifying both sides of the equation.

On the left side, we have: 5/2t - t

To combine these terms, we need a common denominator, which is 2t. So, we rewrite 5/2t as (5 * t) / (2 * t):

(5 * t) / (2 * t) - t

Now, we can subtract the t terms:

(5t - 2t) / (2t) - t

Simplifying further, we have:

3t / (2t) - t

On the right side of the equation, we have: 3 + 3/2t

Since there's already a common denominator, we can directly work with this expression.

Next, let's rewrite the equation with the simplified expressions:

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

Simplifying further, we have:

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

Now, let's combine the t terms on the left side:

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

Simplifying:

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

Now, we need to eliminate the denominator on the left side by multiplying both sides by 2t:

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

Simplifying, we have:

- t = 6t + 3

Next, let's isolate the variable by moving the terms with "t" to one side:

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

Simplifying the equation:

- 7t = 3

Finally, let's solve for "t" by dividing both sides of the equation by -7:

t = 3 / -7

The solution is t = -3/7.

Remember to always double-check your solution by substituting the value of "t" back into the original equation.