Question14. $5-9 k+1+k-2(7-k)$

Studdy Solution

STEP 1

What is this asking? Simplify this algebraic expression with the variable $k$ . Watch out! Don't forget to distribute correctly, especially with that sneaky negative sign!

STEP 2

1. Combine like terms within the parentheses.
2. Distribute the $-2$ .
3. Combine all like terms.

STEP 3

Inside the parentheses, we have $7 - k$ .
There are no like terms to combine here, so we'll leave it as is for now.
But, keeping an eye out for these small simplifications is always a good habit!

STEP 4

Now, let's distribute that $-2$ across the terms inside the parentheses.
Remember, distributing means multiplying each term inside the parentheses by the term outside.
So, we have $-2 \cdot 7$ and $-2 \cdot (-k)$ .

STEP 5

$-2 \cdot 7 = \mathbf{-14}$ .
Don't lose that negative sign!

STEP 6

$-2 \cdot (-k) = \mathbf{2k}$ .
A negative times a negative is a positive!
So, our expression now looks like $5 - 9k + 1 + k - 14 + 2k$ .

STEP 7

Let's gather all the terms with $k$ together.
We have $-9k$ , $k$ , and $2k$ .
Think of this as: $-9 + 1 + 2$ .

STEP 8

$-9 + 1 = -8$ .
Then, $-8 + 2 = \mathbf{-6}$ .
So, combining the $k$ terms gives us $\mathbf{-6k}$ .

STEP 9

Now, let's wrangle those constant terms!
We have $5$ , $1$ , and $-14$ .

STEP 10

$5 + 1 = 6$ .
Then, $6 - 14 = \mathbf{-8}$ .

STEP 11

Putting it all together, our simplified expression is $\mathbf{-6k - 8}$ .

STEP 12

The simplified expression is $-6k - 8$ .

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