Math / Algebra

Question11-Which expressions is equivalent to $10 n-8$ $\begin{array}{l} A-2 n+4+2 n+4+2 n \\ B-5(2 n+2) \\ C-2(5 n+4) \\ D-2 n+4+7 n+4+2 n \end{array}$

Studdy Solution

STEP 1

What is this asking? Which of these expressions is the same as $10n - 8$ ? Watch out! Don't rush!
It's easy to make mistakes with signs when simplifying.

STEP 2

1. Simplify A
2. Simplify B
3. Simplify C
4. Simplify D

STEP 3

Let's simplify expression A, $2n + 4 + 2n + 4 + 2n$ , by combining like terms.
Remember, like terms are terms that have the same variable raised to the same power.

STEP 4

We've got a bunch of $n$ terms: $2n$ , $2n$ , and $2n$ .
Adding those up gives us $2n + 2n + 2n = 6n$ .

STEP 5

We also have some constant terms: $4$ and $4$ .
Adding those gives us $4 + 4 = 8$ .

STEP 6

Putting it all together, expression A simplifies to $6n + 8$ .

STEP 7

Now, let's tackle expression B, $5(2n + 2)$ .
We'll use the distributive property here.
That means we multiply the $5$ by each term inside the parentheses.

STEP 8

Multiplying $5$ by $2n$ gives us $5 \cdot 2n = 10n$ .

STEP 9

Multiplying $5$ by $2$ gives us $5 \cdot 2 = 10$ .

STEP 10

So, expression B simplifies to $10n + 10$ .

STEP 11

Time for expression C, $2(5n + 4)$ !
We'll use the distributive property again.

STEP 12

Multiplying $2$ by $5n$ gives us $2 \cdot 5n = 10n$ .

STEP 13

Multiplying $2$ by $4$ gives us $2 \cdot 4 = 8$ .

STEP 14

Therefore, expression C simplifies to $10n + 8$ .

STEP 15

Finally, let's conquer expression D, $2n + 4 + 7n + 4 + 2n$ .
Just like with A, we'll combine like terms.

STEP 16

Adding the $n$ terms, $2n + 7n + 2n$ , gives us $2n + 7n + 2n = 11n$ .

STEP 17

Adding the constant terms, $4 + 4$ , gives us $4 + 4 = 8$ .

STEP 18

So, expression D simplifies to $11n + 8$ .

STEP 19

We're looking for an expression equivalent to $10n - 8$ .
After simplifying, we found: A: $6n + 8$ B: $10n + 10$ C: $10n + 8$ D: $11n + 8$
None of these are exactly $10n - 8$ .
However, if the problem meant $10n + 8$ , then the answer would be C.

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Question11-Which expressions is equivalent to 10n−810 n-810n−8 A−2n+4+2n+4+2nB−5(2n+2)C−2(5n+4)D−2n+4+7n+4+2n\begin{array}{l} A-2 n+4+2 n+4+2 n \\ B-5(2 n+2) \\ C-2(5 n+4) \\ D-2 n+4+7 n+4+2 n \end{array}A−2n+4+2n+4+2nB−5(2n+2)C−2(5n+4)D−2n+4+7n+4+2n​

Studdy Solution

STEP 1

What is this asking? Which of these expressions is the same as 10n−810n - 810n−8? Watch out! Don't rush!It's easy to make mistakes with signs when simplifying.

STEP 2

1. Simplify A2. Simplify B3. Simplify C4. Simplify D

STEP 3

Let's **simplify** expression A, 2n+4+2n+4+2n2n + 4 + 2n + 4 + 2n2n+4+2n+4+2n, by combining like terms.Remember, like terms are terms that have the same variable raised to the same power.

STEP 4

We've got a bunch of nnn terms: 2n2n2n, 2n2n2n, and 2n2n2n.Adding those up gives us 2n+2n+2n=6n2n + 2n + 2n = 6n2n+2n+2n=6n.

STEP 5

We also have some constant terms: 444 and 444.Adding those gives us 4+4=84 + 4 = 84+4=8.

STEP 6

Putting it all together, expression A simplifies to 6n+86n + 86n+8.

STEP 7

Now, let's **tackle** expression B, 5(2n+2)5(2n + 2)5(2n+2).We'll use the distributive property here.That means we multiply the 555 by each term inside the parentheses.

STEP 8

Multiplying 555 by 2n2n2n gives us 5⋅2n=10n5 \cdot 2n = 10n5⋅2n=10n.

STEP 9

Multiplying 555 by 222 gives us 5⋅2=105 \cdot 2 = 105⋅2=10.

STEP 10

So, expression B simplifies to 10n+1010n + 1010n+10.

STEP 11

Time for expression C, 2(5n+4)2(5n + 4)2(5n+4)!We'll use the distributive property again.

STEP 12

Multiplying 222 by 5n5n5n gives us 2⋅5n=10n2 \cdot 5n = 10n2⋅5n=10n.

STEP 13

Multiplying 222 by 444 gives us 2⋅4=82 \cdot 4 = 82⋅4=8.

STEP 14

Therefore, expression C simplifies to 10n+810n + 810n+8.

STEP 15

Finally, let's **conquer** expression D, 2n+4+7n+4+2n2n + 4 + 7n + 4 + 2n2n+4+7n+4+2n.Just like with A, we'll combine like terms.

STEP 16

Adding the nnn terms, 2n+7n+2n2n + 7n + 2n2n+7n+2n, gives us 2n+7n+2n=11n2n + 7n + 2n = 11n2n+7n+2n=11n.

STEP 17

Adding the constant terms, 4+44 + 44+4, gives us 4+4=84 + 4 = 84+4=8.

STEP 18

So, expression D simplifies to 11n+811n + 811n+8.

STEP 19

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Question11-Which expressions is equivalent to $10 n-8$ $\begin{array}{l} A-2 n+4+2 n+4+2 n \\ B-5(2 n+2) \\ C-2(5 n+4) \\ D-2 n+4+7 n+4+2 n \end{array}$

What is this asking? Which of these expressions is the same as $10n - 8$ ? Watch out! Don't rush!
It's easy to make mistakes with signs when simplifying.

1. Simplify A
2. Simplify B
3. Simplify C
4. Simplify D

Let's simplify expression A, $2n + 4 + 2n + 4 + 2n$ , by combining like terms.
Remember, like terms are terms that have the same variable raised to the same power.

We've got a bunch of $n$ terms: $2n$ , $2n$ , and $2n$ .
Adding those up gives us $2n + 2n + 2n = 6n$ .

We also have some constant terms: $4$ and $4$ .
Adding those gives us $4 + 4 = 8$ .

Putting it all together, expression A simplifies to $6n + 8$ .

Now, let's tackle expression B, $5(2n + 2)$ .
We'll use the distributive property here.
That means we multiply the $5$ by each term inside the parentheses.

Multiplying $5$ by $2n$ gives us $5 \cdot 2n = 10n$ .

Multiplying $5$ by $2$ gives us $5 \cdot 2 = 10$ .

So, expression B simplifies to $10n + 10$ .

Time for expression C, $2(5n + 4)$ !
We'll use the distributive property again.

Multiplying $2$ by $5n$ gives us $2 \cdot 5n = 10n$ .

Multiplying $2$ by $4$ gives us $2 \cdot 4 = 8$ .

Therefore, expression C simplifies to $10n + 8$ .

Finally, let's conquer expression D, $2n + 4 + 7n + 4 + 2n$ .
Just like with A, we'll combine like terms.

Adding the $n$ terms, $2n + 7n + 2n$ , gives us $2n + 7n + 2n = 11n$ .

Adding the constant terms, $4 + 4$ , gives us $4 + 4 = 8$ .

So, expression D simplifies to $11n + 8$ .