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

May 8, 2018

$75.76 z - 92.02$

Explanation:

Given:

$- 7.7 z + - 10.7 \left(8.6 + - 7.8 z\right)$

Steps:

First, distribute $- 10.7$ to the parentheses

$- 10.7 \left(8.6\right) = - 92.02$
$- 10.7 \left(- 7.8 z\right) = 83.46 z$

You now have an expression that looks like this:

$- 7.7 z + - 92.02 + 83.46 z$

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

$- 7.7 z + 83.46 z + - 92.02$

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 $- 7.7 z + 83.46 z$, which equals $75.76 z$.

Your expression now looks like this:

$75.76 z - 92.02$

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

May 8, 2018

The expression

$75.76 z - 92.02$

Explanation:

You have the expression

$- 7.7 z + \left(- 10.7\right) \left(8.6 + \left(- 7.8 z\right)\right)$

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

$- 7.7 z - 10.7 \left(8.6 - 7.8 z\right)$

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 $- 7.8 z$

$- 10.7 \left(8.6\right) = - 92.02$
$- 10.7 \left(- 7.8 z\right) = 83.46 z$

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

$- 7.7 z - 92.02 + 83.46 z$

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

$83.46 z + \left(- 7.7 z\right) = 83.46 z - 7.7 z = 75.76 z$

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

$75.76 z - 92.02$