How do you combine like terms in #-7.7z + - 10.7( 8.6+ - 7.8z )#?

2 Answers
May 8, 2018

#75.76z - 92.02#

Explanation:

Given:

#-7.7z + -10.7(8.6 + -7.8z)#

Steps:

First, distribute #-10.7# to the parentheses

#-10.7(8.6) = -92.02#
#-10.7(-7.8z) = 83.46z#

You now have an expression that looks like this:

#-7.7z + -92.02 + 83.46z#

You can rearrange the expression to put the like terms next to each other:

#-7.7z + 83.46z + - 92.02#

To finish, use the order of operations, which says that addition and subtraction are to be used from left to right in the expression.
Start by solving #-7.7z + 83.46z#, which equals #75.76z#.

Your expression now looks like this:

#75.76z - 92.02#

This is your final answer, as all like terms have been combined and you can't simplify any further.

May 8, 2018

The expression

#75.76z-92.02#

Explanation:

You have the expression

#-7.7z+(-10.7)(8.6+(-7.8z))#

We can simplify this by realizing that adding by a negative number is the same as subtracting that same number. So now, we have the expression

#-7.7z-10.7(8.6-7.8z)#

In order to add like terms in this expression, you must first use the distributive property to multiply #-10.7# by the values within the parentheses.

First multiply #-10.7# by #8.6#

Then multiply #-10.7# by #-7.8z#

#-10.7(8.6)=-92.02#
#-10.7(-7.8z)=83.46z#

Now we can put the products we just found back into the expression. The expression we have now is

#-7.7z-92.02+83.46z#

The final step is to combine like terms in order to simplify the expression.

#83.46z+(-7.7z)=83.46z-7.7z=75.76z#

#-92.02#
*has no like terms to combine with so it simply remains the same

And your final expression is

#75.76z-92.02#