QuestionChoose the equivalent expressions for $3(3 v+1)+4$ . Options include:
1. $(3 v+1) 3+4$
2. $3(2 v+v+1)+4$
3. $1(3 v+3)+4$
4. $3(1+3 v)+4$

Studdy Solution

STEP 1

Assumptions1. We want to find expressions equivalent to $3(3v+1)+4$ . . The expressions are equivalent if they simplify to the same value for any value of $v$ .

STEP 2

The original expression can be simplified by distributing the multiplication across the terms inside the parenthesis.
$(v+1)+4 =9v + +4$

STEP 3

implify the expression further by adding the constants.
$9v +3 + =9v +7$

STEP 4

Now, we will simplify each of the given expressions in the same way and compare them to the original expression $9v +7$ .
First, consider the expression $(3v+1)3+4$ .

STEP 5

istribute the multiplication across the terms inside the parenthesis.
$(3v+1)3+4 =9v +3 +4$

STEP 6

implify the expression by adding the constants.
$9v +3 +4 =9v +$

STEP 7

The expression $(3v+1)3+4$ simplifies to $9v +7$ , which is the same as the original expression. So, $(3v+1)3+4$ is equivalent to the original expression.

STEP 8

Now, consider the expression $3(2v+v+1)+4$ .

STEP 9

implify the expression inside the parenthesis first.
$3(2v+v+)+4 =3(3v+)+4$

STEP 10

istribute the multiplication across the terms inside the parenthesis.
$3(3v+)+4 =9v +3 +4$

STEP 11

implify the expression by adding the constants.
$9v +3 +4 =9v +7$

STEP 12

The expression $(2v+v+)+4$ simplifies to $9v +7$ , which is the same as the original expression. So, $(2v+v+)+4$ is equivalent to the original expression.

STEP 13

Now, consider the expression $(3v+3)+$ .

STEP 14

istribute the multiplication across the terms inside the parenthesis.
$(3v+3)+4 =3v +3 +4$

STEP 15

implify the expression by adding the constants.
$3v +3 +4 =3v +7$

STEP 16

The expression $(3v+3)+4$ simplifies to $3v +$ , which is not the same as the original expression $9v +$ . So, $(3v+3)+4$ is not equivalent to the original expression.

STEP 17

Finally, consider the expression $3(+3v)+4$ .

STEP 18

istribute the multiplication across the terms inside the parenthesis.
$3(+3v)+4 =3 +v +4$

STEP 19

implify the expression by adding the constants.
$3 +9v +4 =9v +7$

STEP 20

The expression $3(+3v)+4$ simplifies to $9v +7$ , which is the same as the original expression. So, $3(+3v)+4$ is equivalent to the original expression.
The expressions equivalent to $3(3v+)+4$ are $(3v+)3+4$ , $3(v+v+)+4$ , and $3(+3v)+4$ .

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