Math / Algebra

QuestionWrite the English phrase as an algebraic expression. Then simplify the expression. Let $x$ represent the number. Eight times the product of negative six and a number.
What is the algebraic expression? $\square$ (Do not simplify.) What is the simplified expression? $\square$

Studdy Solution

STEP 1

What is this asking? We need to translate "eight times the product of negative six and a number" into math, using $x$ for the number, and then simplify the result. Watch out! The word "product" is a big clue, and it's easy to mess up the order of operations if we're not careful!

STEP 2

1. Translate to an algebraic expression.
2. Simplify the expression.

STEP 3

The phrase "product of negative six and a number" translates to $-6 \cdot x$ .
Remember, "product" means multiplication!

STEP 4

The phrase says "eight times the product...".
This means we multiply the entire product from the previous sub-step by eight: $8 \cdot (-6 \cdot x)$ .

STEP 5

We have $8 \cdot (-6 \cdot x)$ .
We can rearrange this using the associative property of multiplication as $(8 \cdot -6) \cdot x$ .
Multiplying $8$ and $-6$ gives us $-48$ .

STEP 6

So, our simplified expression is $-48 \cdot x$ , which we can write more concisely as $-48x$ .

STEP 7

The algebraic expression is $8 \cdot (-6 \cdot x)$ . The simplified expression is $-48x$ .

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QuestionWrite the English phrase as an algebraic expression. Then simplify the expression. Let $x$ represent the number. Eight times the product of negative six and a number.
What is the algebraic expression? $\square$ (Do not simplify.) What is the simplified expression? $\square$

Studdy Solution

STEP 1

What is this asking? We need to translate "eight times the product of negative six and a number" into math, using $x$ for the number, and then simplify the result. Watch out! The word "product" is a big clue, and it's easy to mess up the order of operations if we're not careful!

STEP 2

1. Translate to an algebraic expression.
2. Simplify the expression.

STEP 3

The phrase "product of negative six and a number" translates to $-6 \cdot x$ .
Remember, "product" means multiplication!

STEP 4

The phrase says "eight times the product...".
This means we multiply the entire product from the previous sub-step by eight: $8 \cdot (-6 \cdot x)$ .

STEP 5

We have $8 \cdot (-6 \cdot x)$ .
We can rearrange this using the associative property of multiplication as $(8 \cdot -6) \cdot x$ .
Multiplying $8$ and $-6$ gives us $-48$ .

STEP 6

So, our simplified expression is $-48 \cdot x$ , which we can write more concisely as $-48x$ .

STEP 7

The algebraic expression is $8 \cdot (-6 \cdot x)$ . The simplified expression is $-48x$ .

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QuestionWrite the English phrase as an algebraic expression. Then simplify the expression. Let xxx represent the number. Eight times the product of negative six and a number.What is the algebraic expression? □\square□ (Do not simplify.) What is the simplified expression? □\square□

Studdy Solution

STEP 1

What is this asking? We need to translate "eight times the product of negative six and a number" into math, using xxx for the number, and then simplify the result. Watch out! The word "product" is a big clue, and it's easy to mess up the order of operations if we're not careful!

STEP 2

1. Translate to an algebraic expression.2. Simplify the expression.

STEP 3

The phrase "**product of negative six and a number**" translates to −6⋅x-6 \cdot x−6⋅x.Remember, "product" means multiplication!

STEP 4

The phrase says "**eight times** the product...".This means we multiply the entire product from the previous sub-step by **eight**: 8⋅(−6⋅x)8 \cdot (-6 \cdot x)8⋅(−6⋅x).

STEP 5

We have 8⋅(−6⋅x)8 \cdot (-6 \cdot x)8⋅(−6⋅x).We can rearrange this using the *associative property* of multiplication as (8⋅−6)⋅x(8 \cdot -6) \cdot x(8⋅−6)⋅x.Multiplying 888 and −6-6−6 gives us −48-48−48.

STEP 6

So, our simplified expression is −48⋅x-48 \cdot x−48⋅x, which we can write more concisely as −48x-48x−48x.

STEP 7

The algebraic expression is 8⋅(−6⋅x)8 \cdot (-6 \cdot x)8⋅(−6⋅x). The simplified expression is −48x-48x−48x.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionWrite the English phrase as an algebraic expression. Then simplify the expression. Let $x$ represent the number. Eight times the product of negative six and a number.
What is the algebraic expression? $\square$ (Do not simplify.) What is the simplified expression? $\square$

What is this asking? We need to translate "eight times the product of negative six and a number" into math, using $x$ for the number, and then simplify the result. Watch out! The word "product" is a big clue, and it's easy to mess up the order of operations if we're not careful!

1. Translate to an algebraic expression.
2. Simplify the expression.

The phrase "product of negative six and a number" translates to $-6 \cdot x$ .
Remember, "product" means multiplication!

The phrase says "eight times the product...".
This means we multiply the entire product from the previous sub-step by eight: $8 \cdot (-6 \cdot x)$ .

We have $8 \cdot (-6 \cdot x)$ .
We can rearrange this using the associative property of multiplication as $(8 \cdot -6) \cdot x$ .
Multiplying $8$ and $-6$ gives us $-48$ .

So, our simplified expression is $-48 \cdot x$ , which we can write more concisely as $-48x$ .

The algebraic expression is $8 \cdot (-6 \cdot x)$ . The simplified expression is $-48x$ .