a+8=12
t+(-3)=8
You have $\displaystyle a+8=12$.
If two things are equal if you take the same thing from both the two results
are still equal.
So here we take (subtract) $\displaystyle 8$ form $\displaystyle a+8$ and also from $\displaystyle 12$, and the two results will be equal:
$\displaystyle
(a+8)-8=12-8
$
which gives:
$\displaystyle a=4$.
This is the same thing as: $\displaystyle t-3=8$t+(-3)=8
Here we do the same sort of thing, we add $\displaystyle 3$ to $\displaystyle t-3$ and $\displaystyle 8$ to get:
$\displaystyle (t-3)+3=8+3$
which gives:
$\displaystyle t=11$
RonL
Whatever you do to one side of the equation, you must do to the other:
$\displaystyle a + 8 = 12$
$\displaystyle a + 8 - 8 = 12 - 8$
$\displaystyle a = 4$
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$\displaystyle t+(-3)=8$
$\displaystyle t - 3 = 8$
$\displaystyle t - 3 + 3 = 8 + 3$
$\displaystyle t = 11$
-Dan