First, simplify the innermost brackets:
[-30] + [13 + [-3]] = [-30] + [13 - 3]
Next, perform the addition inside the brackets:
[-30] + [13 - 3] = [-30] + [10]
Now, simplify further by removing the brackets:
[-30] + [10] = -30 + 10
Finally, perform the addition:
-30 + 10 = -20
Therefore, the left-hand side (LHS) of the equation simplifies to -20.
Now, let's simplify the right-hand side (RHS) of the equation:
[-30] + [-3] = -30 + (-3)
Performing the addition:
-30 + (-3) = -33
Therefore, the right-hand side (RHS) of the equation simplifies to -33.
Since -20 is not equal to -33, we can conclude that the given equation is not true. Hence, the statement "[-30] + [13 + [-3]] = [-30] + [-3]" is false.