How do you simplify #(3/4)abs4 + (-3) – (-1)#?

2 Answers
Jul 7, 2015

#(3/4)abs(4)+(-3)-(-1) = 1#

Explanation:

Evaluate the function abs first
Since #abs(4) = 4#
The expression becomes
#color(white)("XXXX")##(3/4)(4)+(-3)-(-1)#

Evaluate the multiplication next
Since #(3/4)(4) = 3#
The expression becomes
#color(white)("XXXX")##3+(-3)-(-1)#

Evaluate addition and subtraction starting from the left
Since #3+(-3) = 0#
The expression becomes
#color(white)("XXXX")##0-(-1)#

Perform the final subtraction
Since #-(-1) = +1#
The expression reduces to
#color(white)("XXXX")##1#

Jul 11, 2015

#(3/4)*|4|+(-3)-(-1)=1#

Explanation:

1.) First, let's look at "the absolute value" of #4#

Recall that "the absolute value" of something is something and "the absolute value" of (negative)something is something:

|something| = something
|-something| = something

So, #|4| = 4#

2.) So, the #(3/4)*|4|# part becomes #(3/4)*4# which is #3#

(Those #4#'s cancel out)

3.) Now, we are left with:

#3+(-3)-(-1)#

The #+(-3)# is just #-3#

because (plus) a (negative)something is (negative)something:

#+(-#something#) = -#something

and the #-(-1)# is just #+1#

because (minus) a (negative)something is (positive)something:

#-(-#something#) = +#something

4.) So, now we have:

#3-3+1#

#3-3# is #0# and we are then left with #1#

So, #1# is our answer (our simplified junk from above)