Question

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

Answer 1

`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.

Answer 2

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`