QuestionFind expressions equivalent to $5(6 b+9)+4$ . Choices: $49 b+30$ , $30 b+49$ , $5(9+6 b)+4$ , $6 b+49$ .

Studdy Solution

STEP 1

Assumptions1. We are looking for expressions that are equivalent to $5(6 b+9)+4$ . . The expressions are equivalent if they simplify to the same value for any value of $b$ .

STEP 2

First, let's simplify the given expression $5(6 b+9)+4$ by using the distributive property of multiplication over addition.
$5(6 b+9)+4 =5 \times6b +5 \times9 +4$

STEP 3

Now, perform the multiplication operations.
$5 \times6b +5 \times9 + =30b +45 +$

STEP 4

Combine the constant terms.
$30b +45 +4 =30b +49$

STEP 5

Now, let's compare the simplified expression $30b +49$ with each of the provided expressions.
First, compare with $49 b+30$ .
$30b +49 \neq49 b+30$ So, $49 b+30$ is not equivalent to the given expression.

STEP 6

Next, compare with $30 b+49$ .
$30b +49 =30 b+49$ So, $30 b+49$ is equivalent to the given expression.

STEP 7

Next, compare with $5(9+6 b)+4$ .
We can simplify $5(9+6 b)+4$ in the same way as we did for the given expression.
$5(9+6 b)+4 =5 \times9 +5 \times6b +4 =45 +30b +4 =30b +49$ So, $5(9+6 b)+4$ is equivalent to the given expression.

STEP 8

Finally, compare with $6 b+49$ .
$30b +49 \neq6 b+49$ So, $6 b+49$ is not equivalent to the given expression.
The expressions equivalent to $5(6 b+)+4$ are $30 b+49$ and $5(+6 b)+4$ .

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