When evaluating the following expression, which operations must be done first, third, and fifth?: #3-2*(2+4)+5-(3/2)^3#

Answer 1

First: addition inside the bracket.
Third: multiplication
Fifth: addition

We follow the Order of Operations, also known as PEMDAS:

So in the expression

#3-2xx(2+4)+5-(3/2)^3#

we first look for #color(red)(P)#. There are two of them: #2+4# and a fraction #3/2#. We can't really do anything with the fraction for now, so let's do #2+4# first:

#3-2xx(6)+5-(3/2)^3#

Now we look for #color(blue)(E)#, which brings us back to that fraction:

#3-2xx(6)+5-27/8#

Next we look for #color(green)(M)# and #color(green)(D)# - and we have #2xx6#, which we'll be doing third

#3-12+5-27/8#

Now we do our #color(brown)(A)# and #color(brown)(S)#, working from left to right. So the fourth thing we do is #3-12#:

#-9+5-27/8#

and the fifth thing we do is #-9+5#

#-4-27/8#

And to finish this off:

#-32/8-27/8=-59/8#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.