Math / Algebra

Question10. Which of the following expressions is equivalent to $3.5(4x - 16) + (-2x)$ ? A $14x - 56$ B $12x - 16$ C $14x - 16$ D $12x - 56$

Studdy Solution

STEP 1

What is this asking? We need to simplify the expression $3.5(4x - 16) + (-2x)$ and find the matching option. Watch out! Don't forget to distribute correctly and combine like terms carefully!

STEP 2

1. Distribute and Simplify
2. Combine Like Terms

STEP 3

Alright, let's distribute that $3.5$ to both terms inside the parentheses $(4x - 16)$ .
Remember, distributing means multiplying each term inside the parentheses by the number outside.
So, we have $3.5 \cdot 4x$ and $3.5 \cdot (-16)$ .

STEP 4

$3.5 \cdot 4x = 14x$ .
See? Not so bad!

STEP 5

$3.5 \cdot (-16) = -56$ .
Don't drop that minus sign!

STEP 6

So, after distributing, our expression becomes $14x - 56 + (-2x)$ .
Looking good so far!

STEP 7

Remember, like terms are terms that have the same variable raised to the same power.
In our expression, $14x$ and $-2x$ are like terms.

STEP 8

Let's combine those $x$ terms: $14x + (-2x) = 12x$ .
We're almost there!

STEP 9

Now, our expression is $12x - 56$ .
Much simpler, right?

STEP 10

Our simplified expression is $12x - 56$ , which matches option D.
We did it!

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Question10. Which of the following expressions is equivalent to $3.5(4x - 16) + (-2x)$ ? A $14x - 56$ B $12x - 16$ C $14x - 16$ D $12x - 56$

Studdy Solution

STEP 1

What is this asking? We need to simplify the expression $3.5(4x - 16) + (-2x)$ and find the matching option. Watch out! Don't forget to distribute correctly and combine like terms carefully!

STEP 2

1. Distribute and Simplify
2. Combine Like Terms

STEP 3

Alright, let's distribute that $3.5$ to both terms inside the parentheses $(4x - 16)$ .
Remember, distributing means multiplying each term inside the parentheses by the number outside.
So, we have $3.5 \cdot 4x$ and $3.5 \cdot (-16)$ .

STEP 4

$3.5 \cdot 4x = 14x$ .
See? Not so bad!

STEP 5

$3.5 \cdot (-16) = -56$ .
Don't drop that minus sign!

STEP 6

So, after distributing, our expression becomes $14x - 56 + (-2x)$ .
Looking good so far!

STEP 7

Remember, like terms are terms that have the same variable raised to the same power.
In our expression, $14x$ and $-2x$ are like terms.

STEP 8

Let's combine those $x$ terms: $14x + (-2x) = 12x$ .
We're almost there!

STEP 9

Now, our expression is $12x - 56$ .
Much simpler, right?

STEP 10

Our simplified expression is $12x - 56$ , which matches option D.
We did it!

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Question10. Which of the following expressions is equivalent to 3.5(4x−16)+(−2x)3.5(4x - 16) + (-2x)3.5(4x−16)+(−2x)? A 14x−5614x - 5614x−56 B 12x−1612x - 1612x−16 C 14x−1614x - 1614x−16 D 12x−5612x - 5612x−56

Studdy Solution

STEP 1

What is this asking? We need to simplify the expression 3.5(4x−16)+(−2x)3.5(4x - 16) + (-2x)3.5(4x−16)+(−2x) and find the matching option. Watch out! Don't forget to distribute correctly and combine like terms carefully!

STEP 2

1. Distribute and Simplify2. Combine Like Terms

STEP 3

Alright, let's **distribute** that 3.53.53.5 to both terms inside the parentheses (4x−16)(4x - 16)(4x−16).Remember, distributing means multiplying each term inside the parentheses by the number outside.So, we have 3.5⋅4x3.5 \cdot 4x3.5⋅4x and 3.5⋅(−16)3.5 \cdot (-16)3.5⋅(−16).

STEP 4

3.5⋅4x=14x3.5 \cdot 4x = 14x3.5⋅4x=14x.See? Not so bad!

STEP 5

3.5⋅(−16)=−563.5 \cdot (-16) = -563.5⋅(−16)=−56.Don't drop that minus sign!

STEP 6

So, after distributing, our expression becomes 14x−56+(−2x)14x - 56 + (-2x)14x−56+(−2x).Looking good so far!

STEP 7

Remember, **like terms** are terms that have the same variable raised to the same power.In our expression, 14x14x14x and −2x-2x−2x are like terms.

STEP 8

Let's combine those xxx terms: 14x+(−2x)=12x14x + (-2x) = 12x14x+(−2x)=12x.We're almost there!

STEP 9

Now, our expression is 12x−5612x - 5612x−56.Much simpler, right?

STEP 10

Our simplified expression is 12x−5612x - 5612x−56, which matches option **D**.We did it!

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Studdy solves anything!

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Question10. Which of the following expressions is equivalent to $3.5(4x - 16) + (-2x)$ ? A $14x - 56$ B $12x - 16$ C $14x - 16$ D $12x - 56$

What is this asking? We need to simplify the expression $3.5(4x - 16) + (-2x)$ and find the matching option. Watch out! Don't forget to distribute correctly and combine like terms carefully!

1. Distribute and Simplify
2. Combine Like Terms

Alright, let's distribute that $3.5$ to both terms inside the parentheses $(4x - 16)$ .
Remember, distributing means multiplying each term inside the parentheses by the number outside.
So, we have $3.5 \cdot 4x$ and $3.5 \cdot (-16)$ .

$3.5 \cdot 4x = 14x$ .
See? Not so bad!

$3.5 \cdot (-16) = -56$ .
Don't drop that minus sign!

So, after distributing, our expression becomes $14x - 56 + (-2x)$ .
Looking good so far!

Remember, like terms are terms that have the same variable raised to the same power.
In our expression, $14x$ and $-2x$ are like terms.

Let's combine those $x$ terms: $14x + (-2x) = 12x$ .
We're almost there!

Now, our expression is $12x - 56$ .
Much simpler, right?

Our simplified expression is $12x - 56$ , which matches option D.
We did it!