Math / Algebra

QuestionSimplify the expression: $3(d-4) + 2 - 2d + 1 - d$

Studdy Solution

STEP 1

What is this asking? We need to simplify this expression with the variable $d$ , making it as short and sweet as possible! Watch out! Don't forget to distribute correctly and pay attention to the signs of each term.
Those little negative signs can be sneaky!

STEP 2

1. Distribute and Simplify
2. Combine Like Terms

STEP 3

Let's distribute that $3$ across the parentheses $(d-4)$ .
Remember, distributing means multiplying the $3$ by each term inside the parentheses.
This is because of the distributive property of multiplication over addition (and subtraction).
So, $3(d-4)$ becomes $3 \cdot d - 3 \cdot 4$ , which simplifies to $3d - 12$ .

STEP 4

Now, let's rewrite the entire expression with the simplified part: $3d - 12 + 2 - 2d + 1 - d$ .
Look how much cleaner that looks already!

STEP 5

Let's bring all the terms with $d$ together.
We have $3d$ , $-2d$ , and $-d$ .
Think of these as different piles of "d-stuff".

STEP 6

Now, let's add those "d-stuff" piles together: $3d - 2d - d = (3-2-1)d = 0d = 0$ .
Wow, the $d$ terms add to zero and disappear!

STEP 7

Let's round up those constant terms (the numbers without $d$ ): $-12$ , $2$ , and $1$ .

STEP 8

Adding those constants gives us $-12 + 2 + 1 = -9$ .

STEP 9

So, after all that simplifying, our final answer is $-9$ !

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QuestionSimplify the expression: $3(d-4) + 2 - 2d + 1 - d$

Studdy Solution

STEP 1

What is this asking? We need to simplify this expression with the variable $d$ , making it as short and sweet as possible! Watch out! Don't forget to distribute correctly and pay attention to the signs of each term.
Those little negative signs can be sneaky!

STEP 2

1. Distribute and Simplify
2. Combine Like Terms

STEP 3

STEP 4

Now, let's rewrite the entire expression with the simplified part: $3d - 12 + 2 - 2d + 1 - d$ .
Look how much cleaner that looks already!

STEP 5

Let's bring all the terms with $d$ together.
We have $3d$ , $-2d$ , and $-d$ .
Think of these as different piles of "d-stuff".

STEP 6

Now, let's add those "d-stuff" piles together: $3d - 2d - d = (3-2-1)d = 0d = 0$ .
Wow, the $d$ terms add to zero and disappear!

STEP 7

Let's round up those constant terms (the numbers without $d$ ): $-12$ , $2$ , and $1$ .

STEP 8

Adding those constants gives us $-12 + 2 + 1 = -9$ .

STEP 9

So, after all that simplifying, our final answer is $-9$ !

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QuestionSimplify the expression: 3(d−4)+2−2d+1−d3(d-4) + 2 - 2d + 1 - d3(d−4)+2−2d+1−d

Studdy Solution

STEP 1

What is this asking? We need to simplify this expression with the variable ddd, making it as short and sweet as possible! Watch out! Don't forget to distribute correctly and pay attention to the signs of each term.Those little negative signs can be sneaky!

STEP 2

1. Distribute and Simplify2. Combine Like Terms

STEP 3

STEP 4

Now, let's rewrite the *entire* expression with the simplified part: 3d−12+2−2d+1−d3d - 12 + 2 - 2d + 1 - d3d−12+2−2d+1−d.Look how much cleaner that looks already!

STEP 5

Let's bring all the terms with ddd together.We have 3d3d3d, −2d-2d−2d, and −d-d−d.Think of these as different piles of "d-stuff".

STEP 6

Now, let's add those "d-stuff" piles together: 3d−2d−d=(3−2−1)d=0d=03d - 2d - d = (3-2-1)d = 0d = 03d−2d−d=(3−2−1)d=0d=0.Wow, the ddd terms add to zero and disappear!

STEP 7

Let's round up those constant terms (the numbers without ddd): −12-12−12, 222, and 111.

STEP 8

Adding those constants gives us −12+2+1=−9-12 + 2 + 1 = -9−12+2+1=−9.

STEP 9

So, after all that simplifying, our final answer is −9-9−9!

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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.

QuestionSimplify the expression: $3(d-4) + 2 - 2d + 1 - d$

What is this asking? We need to simplify this expression with the variable $d$ , making it as short and sweet as possible! Watch out! Don't forget to distribute correctly and pay attention to the signs of each term.
Those little negative signs can be sneaky!

1. Distribute and Simplify
2. Combine Like Terms

Now, let's rewrite the entire expression with the simplified part: $3d - 12 + 2 - 2d + 1 - d$ .
Look how much cleaner that looks already!

Let's bring all the terms with $d$ together.
We have $3d$ , $-2d$ , and $-d$ .
Think of these as different piles of "d-stuff".

Now, let's add those "d-stuff" piles together: $3d - 2d - d = (3-2-1)d = 0d = 0$ .
Wow, the $d$ terms add to zero and disappear!

Let's round up those constant terms (the numbers without $d$ ): $-12$ , $2$ , and $1$ .

Adding those constants gives us $-12 + 2 + 1 = -9$ .

So, after all that simplifying, our final answer is $-9$ !