Using a number line, solve (-8) + (-4) + 6. Verify the associative identity of addition for integers -8, -4 and 6.

To add a positive integer, we move to the right on the number line. To add a negative integer, we move to the left on the number line.

(i) Start at -8 on the number line and move 4 units to the left:

-8 → -9 → -10 → -11 → -12.

(-8) + (-4) = -12

(ii) Start at -12 on the number line and move 6 units to the right:

-12 → -11 → -10 → -9 → -8 → −7 → −6.

(-12) + 6 = -6

Verification of associative property : The associative property states that [a + b] + c = a + [b + c].

Taking a = -8, b = -4 and c = 6 :

L.H.S. = [(-8) + (-4)] + 6 = (-12) + 6 = -6.

R.H.S. = (-8) + [(-4) + 6] = (-8) + 2 = -6.

Since L.H.S. = R.H.S. = -6, the associative property is verified.

Hence, (-8) + (-4) + 6 = -6 and the associative property of addition is verified.