Here is how I would approach this-
Since the right side of the equation has the most extra "stuff" to get rid of, I'll start from that side.
1) First, you would need to subtract 7 from each side of the equation, to get rid of the "+7" at the end. Once you have subtracted the 7 from both sides, you are left with 4t+7= 6t/5
2) Since our goal is to isolate the terms with t, so we can add them together, we need to get rid of the "/5" on the "6t/5" term. To do this, multiply each side of the equation by 5. Once each term on both sides of the equation has been multiplied by 5, you are left with 20t+35=6t
3) In order to combine both sets of "t" terms onto one side of the equation, either the 20t or the 6t has to move. For this problem, we will move the 6t. To move the 6t, we subtract it from both sides, leaving us with 14t+35=0.
4) To solve for t, subtract 35 from each side, resulting in an equation that looks like this-> 14t=-35
5) Then we must divide each side of the equation by 14 to determine the value of just t.
6) After we divide both sides by 14, our equation becomes t= -35/14.
7) Most teachers will want the answer reduced as far as possible, so t= -35/14 is not quite finished. If you recall, 35 and 14 are both factorable by 7, meaning that "some number" times 7 is 35, and "some number" times 7 is 14. Since both numbers are factorable by 7, divide the top (numerator) and bottom (denominator) by 7, leaving you with t= -5/2
To check your work, take -5/2 and plug it into the original equation in place of each t, like below:
4(-5/2)+ 14= 6(-5/2) /5 +7
Multiplying out the numbers, you get (-20/2)+14= (-30/10) +7
Simplifying the two sides, you get 4 (because -10+14 is 4) = 4 (because -3+7 is 4)
Since you are left with 4=4, you know you have done it correctly, because they are equal. If, for instance, you had gotten this far and had come up with 4=8, something was wrong in your mathematics, because 4=8 is a false statement.