Math / Algebra

Question10. Are $9x \cdot 8$ and $81x$ equivalent expressions? Explain.

Studdy Solution

STEP 1

What is this asking? Are $9x \cdot 8$ and $81x$ the same?
Why or why not? Watch out! Don't mix up multiplication and addition!
We're dealing with multiplication here, so be careful not to accidentally add things.

STEP 2

1. Simplify the first expression
2. Compare the simplified expressions

STEP 3

Let's look at our first expression, $9x \cdot 8$ .
We can rewrite this as $9 \cdot x \cdot 8$ , making it super clear what we're multiplying!

STEP 4

Now, remember the commutative property of multiplication?
It says we can multiply numbers in any order we want!
So, let's rearrange things to make the calculation easier: $9 \cdot 8 \cdot x$ .

STEP 5

Now, let's multiply the constants $9$ and $8$ .
What's $9 \cdot 8$ ?
It's 72!
So, our expression becomes $72 \cdot x$ , which we can write simply as $72x$ .

STEP 6

We've simplified $9x \cdot 8$ to $72x$ .
The other expression is $81x$ .

STEP 7

Now, let's compare!
We have $72x$ and $81x$ .
The coefficient of $x$ in the first expression is 72, and the coefficient of $x$ in the second expression is 81.

STEP 8

Are 72 and 81 the same number?
Nope! They're totally different!
So, $72x$ and $81x$ are not equivalent expressions.

STEP 9

$9x \cdot 8$ and $81x$ are not equivalent.
We simplified $9x \cdot 8$ to $72x$ , and $72x$ is not the same as $81x$ .

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Question10. Are $9x \cdot 8$ and $81x$ equivalent expressions? Explain.

Studdy Solution

STEP 1

What is this asking? Are $9x \cdot 8$ and $81x$ the same?
Why or why not? Watch out! Don't mix up multiplication and addition!
We're dealing with multiplication here, so be careful not to accidentally add things.

STEP 2

1. Simplify the first expression
2. Compare the simplified expressions

STEP 3

Let's look at our first expression, $9x \cdot 8$ .
We can rewrite this as $9 \cdot x \cdot 8$ , making it super clear what we're multiplying!

STEP 4

Now, remember the commutative property of multiplication?
It says we can multiply numbers in any order we want!
So, let's rearrange things to make the calculation easier: $9 \cdot 8 \cdot x$ .

STEP 5

Now, let's multiply the constants $9$ and $8$ .
What's $9 \cdot 8$ ?
It's 72!
So, our expression becomes $72 \cdot x$ , which we can write simply as $72x$ .

STEP 6

We've simplified $9x \cdot 8$ to $72x$ .
The other expression is $81x$ .

STEP 7

Now, let's compare!
We have $72x$ and $81x$ .
The coefficient of $x$ in the first expression is 72, and the coefficient of $x$ in the second expression is 81.

STEP 8

Are 72 and 81 the same number?
Nope! They're totally different!
So, $72x$ and $81x$ are not equivalent expressions.

STEP 9

$9x \cdot 8$ and $81x$ are not equivalent.
We simplified $9x \cdot 8$ to $72x$ , and $72x$ is not the same as $81x$ .

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Question10. Are 9x⋅89x \cdot 89x⋅8 and 81x81x81x equivalent expressions? Explain.

Studdy Solution

STEP 1

What is this asking? Are 9x⋅89x \cdot 89x⋅8 and 81x81x81x the same?Why or why not? Watch out! Don't mix up multiplication and addition!We're dealing with multiplication here, so be careful not to accidentally add things.

STEP 2

1. Simplify the first expression2. Compare the simplified expressions

STEP 3

Let's look at our first expression, 9x⋅89x \cdot 89x⋅8.We can rewrite this as 9⋅x⋅89 \cdot x \cdot 89⋅x⋅8, making it super clear what we're multiplying!

STEP 4

Now, remember the *commutative property* of multiplication?It says we can multiply numbers in any order we want!So, let's rearrange things to make the calculation easier: 9⋅8⋅x9 \cdot 8 \cdot x9⋅8⋅x.

STEP 5

Now, let's **multiply** the **constants** 999 and 888.What's 9⋅89 \cdot 89⋅8?It's **72**!So, our expression becomes 72⋅x72 \cdot x72⋅x, which we can write simply as 72x72x72x.

STEP 6

We've simplified 9x⋅89x \cdot 89x⋅8 to 72x72x72x.The other expression is 81x81x81x.

STEP 7

Now, let's compare!We have 72x72x72x and 81x81x81x.The *coefficient* of xxx in the first expression is **72**, and the *coefficient* of xxx in the second expression is **81**.

STEP 8

Are **72** and **81** the same number?Nope! They're totally different!So, 72x72x72x and 81x81x81x are *not* equivalent expressions.

STEP 9

9x⋅89x \cdot 89x⋅8 and 81x81x81x are **not equivalent**.We simplified 9x⋅89x \cdot 89x⋅8 to 72x72x72x, and 72x72x72x is not the same as 81x81x81x.

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Question10. Are $9x \cdot 8$ and $81x$ equivalent expressions? Explain.

What is this asking? Are $9x \cdot 8$ and $81x$ the same?
Why or why not? Watch out! Don't mix up multiplication and addition!
We're dealing with multiplication here, so be careful not to accidentally add things.

1. Simplify the first expression
2. Compare the simplified expressions

Let's look at our first expression, $9x \cdot 8$ .
We can rewrite this as $9 \cdot x \cdot 8$ , making it super clear what we're multiplying!

Now, remember the commutative property of multiplication?
It says we can multiply numbers in any order we want!
So, let's rearrange things to make the calculation easier: $9 \cdot 8 \cdot x$ .

Now, let's multiply the constants $9$ and $8$ .
What's $9 \cdot 8$ ?
It's 72!
So, our expression becomes $72 \cdot x$ , which we can write simply as $72x$ .

We've simplified $9x \cdot 8$ to $72x$ .
The other expression is $81x$ .

Now, let's compare!
We have $72x$ and $81x$ .
The coefficient of $x$ in the first expression is 72, and the coefficient of $x$ in the second expression is 81.

Are 72 and 81 the same number?
Nope! They're totally different!
So, $72x$ and $81x$ are not equivalent expressions.

$9x \cdot 8$ and $81x$ are not equivalent.
We simplified $9x \cdot 8$ to $72x$ , and $72x$ is not the same as $81x$ .