Question

Explain whether 13.1tminus2.9t is equivalent to 2.9tminus13.1t or not. Support your answer by evaluating the expressions for tequals2.

Answer 1

They are not equivalent. Subtraction is not commutative, so switching the order changes the sign.

Algebraically:
13.1t − 2.9t = (13.1 − 2.9)t = 10.2t,
2.9t − 13.1t = (2.9 − 13.1)t = −10.2t = −(13.1t − 2.9t).

For t = 2:
13.1(2) − 2.9(2) = 10.2 × 2 = 20.4,
2.9(2) − 13.1(2) = −10.2 × 2 = −20.4.

So the two expressions give 20.4 and −20.4 respectively — they are negatives of each other, not equal.