QuestionChoose the equivalent expressions for $5(8 k+6)+8$ : $38 k+40$ , $(8 k+6) 5+8$ , $40 k+38$ , $5(6+8 k)+8$ .

Studdy Solution

STEP 1

Assumptions1. We are looking for expressions equivalent to $5(8 k+6)+8$ . . Two expressions are equivalent if they simplify to the same form.

STEP 2

First, let's simplify the given expression $5(8 k+6)+8$ .
istribute the5 into the parentheses $5(8 k+6)+8 =58k +56 +8$

STEP 3

Calculate the multiplication $58k +56 +8 =40k +30 +8$

STEP 4

Combine like terms $40k +30 +8 =40k +38$ So, the simplified form of the given expression is $40k +38$ .

STEP 5

Now, let's check each of the provided expressions to see if they simplify to the same form.
First, consider $38 k+40$ . This is not in the same form as $40k +38$ , so it is not equivalent to the given expression.

STEP 6

Next, consider $(8 k+6)5+8$ .istribute the5 into the parentheses $(8 k+6)5+8 =58k +56 +8$

STEP 7

Calculate the multiplication $5k +56 + =40k +30 +$

STEP 8

Combine like terms $40k +30 +8 =40k +38$ So, $(8 k+6)5+8$ is equivalent to the given expression.

STEP 9

Next, consider $40 k+38$ . This is already in the same form as $40k +38$ , so it is equivalent to the given expression.

STEP 10

Finally, consider $5(6+8 k)+8$ .istribute the5 into the parentheses $5(6+8 k)+8 =56 +58k +8$

STEP 11

Calculate the multiplication $56 +58k +8 =30 +40k +8$

STEP 12

Rearrange the terms $30 +40k +8 =40k +30 +8$

STEP 13

Combine like terms $40k +30 +8 =40k +38$ So, $5(6+8 k)+8$ is equivalent to the given expression.
So, the expressions that are equivalent to $5(8 k+6)+8$ are $(8 k+6)5+8$ , $40 k+38$ , and $5(6+8 k)+8$ .

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