Question(12.) $-2.5(-3+4 n+8)$

Studdy Solution

STEP 1

What is this asking? We need to simplify this expression with a variable $n$ inside the parentheses. Watch out! Don't forget the order of operations (PEMDAS/BODMAS)!
Also, be super careful with those negative signs; they can be sneaky!

STEP 2

1. Simplify Inside Parentheses
2. Distribute

STEP 3

Alright, let's kick things off inside those parentheses!
We've got $-3 + 4n + 8$ .
Notice we have two constant terms, $-3$ and $8$ , that we can combine!

STEP 4

So, $-3 + 8$ gives us $5$ !
Remember, adding a positive number is the same as subtracting a negative number.
That leaves us with $5 + 4n$ inside the parentheses.
Much cleaner, right?

STEP 5

Now, we've got $-2.5(5 + 4n)$ .
Time to distribute that $-2.5$ to both terms inside the parentheses!
Distributing means multiplying the outside term by each term inside.

STEP 6

First, $-2.5 \cdot 5$ .
This gives us $-12.5$ .
Keep those negative signs in mind!

STEP 7

Next, we have $-2.5 \cdot 4n$ .
Multiplying $-2.5$ by $4$ gives us $-10$ .
So, this term becomes $-10n$ .

STEP 8

Putting it all together, we get $-12.5 - 10n$ , or equivalently $-10n - 12.5$ .
Boom!

STEP 9

Our simplified expression is $-10n - 12.5$ .

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