QuestionChoose the expressions equivalent to $7(3 n+5)+4$ : $(3 n+5) 7+4$ , $21 n+39$ , $5(3 n+7)+4$ , $7(5 n+3)+4$ .

Studdy Solution

STEP 1

Assumptions1. We are looking for expressions that are equivalent to $7(3 n+5)+4$ . . Equivalent expressions will have the same value for all values of $n$ .

STEP 2

We will start by simplifying the given expression $7( n+5)+4$ .
To do this, we distribute the $7$ across the terms inside the parentheses.
7( n+5)+4 =7 \cdotn +7 \cdot5 +4

STEP 3

Now, perform the multiplication to simplify the expression.
$7 \cdot3n +7 \cdot5 + =21n +35 +$

STEP 4

Combine like terms to further simplify the expression.
$21n +35 +4 =21n +39$

STEP 5

Now, we will compare the simplified expression $21n +39$ with each of the provided expressions to see if they are equivalent.
First, compare with $(3 n+5)7+4$ . This expression is just a rearrangement of the original expression, so it is equivalent.

STEP 6

Next, compare with $21 n+39$ . This expression is the same as the simplified expression, so it is equivalent.

STEP 7

Then, compare with $5(3 n+7)+4$ . Distribute the $5$ across the terms inside the parentheses.
$5(3 n+7)+4 =5 \cdot3n +5 \cdot7 +4$

STEP 8

Perform the multiplication to simplify the expression.
$5 \cdot3n +5 \cdot7 +4 =15n +35 +4$

STEP 9

Combine like terms to further simplify the expression.
$15n +35 +4 =15n +39$ This expression is not equivalent to the original expression because the coefficient of $n$ is different.

STEP 10

Finally, compare with $7(5 n+3)+4$ . Distribute the $7$ across the terms inside the parentheses.
$7(5 n+3)+4 =7 \cdot5n +7 \cdot3 +4$

STEP 11

Perform the multiplication to simplify the expression.
$7 \cdot5n +7 \cdot3 +4 =35n +21 +4$

STEP 12

Combine like terms to further simplify the expression.
$35n +21 +4 =35n +25$ This expression is not equivalent to the original expression because the coefficient of $n$ is different and the constant term is also different.
The expressions equivalent to $7( n+5)+4$ are $( n+5)7+4$ and $21 n+39$ .

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