Math / Algebra

QuestionFind an equivalent expression (use the "reverse" method) DO NOT TYPE SPACES $3 j-27=$ $\square$

Studdy Solution

STEP 1

What is this asking? We're asked to rewrite the expression $3j - 27$ by pulling out a common factor, essentially doing the distributive property in reverse! Watch out! Don't forget to check your answer by distributing the factor back into the parentheses.
It should match the original expression!

STEP 2

1. Find the Greatest Common Factor (GCF).
2. Factor out the GCF.

STEP 3

Let's look at our expression: $3j - 27$ .
We need to find the greatest common factor of $3j$ and $27$ .
What's the biggest number that divides evenly into both?

STEP 4

The factors of $3j$ are $1$ , $3$ , and $j$ .
The factors of $27$ are $1$ , $3$ , $9$ , and $27$ .
The greatest common factor is 3!

STEP 5

Now, we're going to factor out our GCF, which is 3.
This means we'll divide each term in our original expression ( $3j - 27$ ) by 3.

STEP 6

Dividing $3j$ by 3 gives us $j$ .
Dividing $-27$ by 3 gives us $-9$ .
So, we have $3(j - 9)$ .

STEP 7

Let's double-check our work!
Distribute the 3 back into the parentheses: $3 \cdot j - 3 \cdot 9 = 3j - 27$ .
Awesome, it matches our original expression!

STEP 8

$3(j-9)$

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QuestionFind an equivalent expression (use the "reverse" method) DO NOT TYPE SPACES $3 j-27=$ $\square$

Studdy Solution

STEP 1

What is this asking? We're asked to rewrite the expression $3j - 27$ by pulling out a common factor, essentially doing the distributive property in reverse! Watch out! Don't forget to check your answer by distributing the factor back into the parentheses.
It should match the original expression!

STEP 2

1. Find the Greatest Common Factor (GCF).
2. Factor out the GCF.

STEP 3

Let's look at our expression: $3j - 27$ .
We need to find the greatest common factor of $3j$ and $27$ .
What's the biggest number that divides evenly into both?

STEP 4

The factors of $3j$ are $1$ , $3$ , and $j$ .
The factors of $27$ are $1$ , $3$ , $9$ , and $27$ .
The greatest common factor is 3!

STEP 5

Now, we're going to factor out our GCF, which is 3.
This means we'll divide each term in our original expression ( $3j - 27$ ) by 3.

STEP 6

Dividing $3j$ by 3 gives us $j$ .
Dividing $-27$ by 3 gives us $-9$ .
So, we have $3(j - 9)$ .

STEP 7

Let's double-check our work!
Distribute the 3 back into the parentheses: $3 \cdot j - 3 \cdot 9 = 3j - 27$ .
Awesome, it matches our original expression!

STEP 8

$3(j-9)$

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QuestionFind an equivalent expression (use the "reverse" method) DO NOT TYPE SPACES 3j−27=3 j-27=3j−27= □\square□

Studdy Solution

STEP 1

STEP 2

1. Find the Greatest Common Factor (GCF).2. Factor out the GCF.

STEP 3

Let's look at our expression: 3j−273j - 273j−27.We need to find the **greatest common factor** of 3j3j3j and 272727.What's the biggest number that divides evenly into both?

STEP 4

The factors of 3j3j3j are 111, 333, and jjj.The factors of 272727 are 111, 333, 999, and 272727.The **greatest common factor** is **3**!

STEP 5

Now, we're going to **factor out** our GCF, which is **3**.This means we'll divide each term in our original expression (3j−273j - 273j−27) by **3**.

STEP 6

Dividing 3j3j3j by **3** gives us jjj.Dividing −27-27−27 by **3** gives us −9-9−9.So, we have 3(j−9)3(j - 9)3(j−9).

STEP 7

Let's **double-check** our work!Distribute the **3** back into the parentheses: 3⋅j−3⋅9=3j−273 \cdot j - 3 \cdot 9 = 3j - 273⋅j−3⋅9=3j−27.Awesome, it matches our original expression!

STEP 8

3(j−9)3(j-9)3(j−9)

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QuestionFind an equivalent expression (use the "reverse" method) DO NOT TYPE SPACES $3 j-27=$ $\square$

1. Find the Greatest Common Factor (GCF).
2. Factor out the GCF.

Let's look at our expression: $3j - 27$ .
We need to find the greatest common factor of $3j$ and $27$ .
What's the biggest number that divides evenly into both?

The factors of $3j$ are $1$ , $3$ , and $j$ .
The factors of $27$ are $1$ , $3$ , $9$ , and $27$ .
The greatest common factor is 3!

Now, we're going to factor out our GCF, which is 3.
This means we'll divide each term in our original expression ( $3j - 27$ ) by 3.

Dividing $3j$ by 3 gives us $j$ .
Dividing $-27$ by 3 gives us $-9$ .
So, we have $3(j - 9)$ .

Let's double-check our work!
Distribute the 3 back into the parentheses: $3 \cdot j - 3 \cdot 9 = 3j - 27$ .
Awesome, it matches our original expression!

$3(j-9)$