Solved on Mar 14, 2024

Add the expressions in the boxes to simplify the given expressions involving $8.41$ , $3b$ , $3.46$ , and $3.78b$ .

STEP 1

Assumptions
1. The expressions involve real numbers.
2. The expressions on both sides of the equation are equal.
3. We are to simplify and combine like terms.

STEP 2

First, we will combine like terms on the left-hand side of the equation. Like terms are terms that have the same variable raised to the same power.
$(8.41 + 3b) + (3.46 + 3.78b)$

STEP 3

Combine the constant terms (terms without variables) on the left-hand side.
$8.41 + 3.46$

STEP 4

Calculate the sum of the constant terms.
$8.41 + 3.46 = 11.87$

STEP 5

Combine the terms with the variable $b$ on the left-hand side.
$3b + 3.78b$

STEP 6

Calculate the sum of the terms with the variable $b$ .
$3b + 3.78b = 6.78b$

STEP 7

Now, we have the simplified left-hand side of the equation.
$11.87 + 6.78b$

STEP 8

Next, we will express the right-hand side of the equation in a similar form to the left-hand side by filling in the boxes with the appropriate terms.
$(3b + \square) + (8.41 + \square)$

STEP 9

From the left-hand side, we know the term that combines with $3b$ is $6.78b$ and the term that combines with $8.41$ is $11.87$ .

STEP 10

Fill in the boxes on the right-hand side with the corresponding terms.
$(3b + 6.78b) + (8.41 + 11.87)$

STEP 11

Now, we have the right-hand side of the equation expressed with the correct terms.
$(3b + 6.78b) + (8.41 + 11.87) = 11.87 + 6.78b$

STEP 12

The final step is to write the simplified expression that represents the sum of both sides of the equation.
$11.87 + 6.78b$
The boxes should be filled with the following values:
$\begin{aligned} (8.41+3 b)+(3.46+3.78 b) & =(3 b+6.78 b)+(8.41+11.87) \\ & =11.87 + 6.78b \end{aligned}$

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Add the expressions in the boxes to simplify the given expressions involving $8.41$ , $3b$ , $3.46$ , and $3.78b$ .

STEP 1

Assumptions
1. The expressions involve real numbers.
2. The expressions on both sides of the equation are equal.
3. We are to simplify and combine like terms.

STEP 2

First, we will combine like terms on the left-hand side of the equation. Like terms are terms that have the same variable raised to the same power.
$(8.41 + 3b) + (3.46 + 3.78b)$

STEP 3

Combine the constant terms (terms without variables) on the left-hand side.
$8.41 + 3.46$

STEP 4

Calculate the sum of the constant terms.
$8.41 + 3.46 = 11.87$

STEP 5

Combine the terms with the variable $b$ on the left-hand side.
$3b + 3.78b$

STEP 6

Calculate the sum of the terms with the variable $b$ .
$3b + 3.78b = 6.78b$

STEP 7

Now, we have the simplified left-hand side of the equation.
$11.87 + 6.78b$

STEP 8

Next, we will express the right-hand side of the equation in a similar form to the left-hand side by filling in the boxes with the appropriate terms.
$(3b + \square) + (8.41 + \square)$

STEP 9

From the left-hand side, we know the term that combines with $3b$ is $6.78b$ and the term that combines with $8.41$ is $11.87$ .

STEP 10

Fill in the boxes on the right-hand side with the corresponding terms.
$(3b + 6.78b) + (8.41 + 11.87)$

STEP 11

Now, we have the right-hand side of the equation expressed with the correct terms.
$(3b + 6.78b) + (8.41 + 11.87) = 11.87 + 6.78b$

STEP 12

The final step is to write the simplified expression that represents the sum of both sides of the equation.
$11.87 + 6.78b$
The boxes should be filled with the following values:
$\begin{aligned} (8.41+3 b)+(3.46+3.78 b) & =(3 b+6.78 b)+(8.41+11.87) \\ & =11.87 + 6.78b \end{aligned}$

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Add the expressions in the boxes to simplify the given expressions involving 8.418.418.41, 3b3b3b, 3.463.463.46, and 3.78b3.78b3.78b.

STEP 1

Assumptions1. The expressions involve real numbers.2. The expressions on both sides of the equation are equal.3. We are to simplify and combine like terms.

STEP 2

First, we will combine like terms on the left-hand side of the equation. Like terms are terms that have the same variable raised to the same power.(8.41+3b)+(3.46+3.78b) (8.41 + 3b) + (3.46 + 3.78b) (8.41+3b)+(3.46+3.78b)

STEP 3

Combine the constant terms (terms without variables) on the left-hand side.8.41+3.46 8.41 + 3.46 8.41+3.46

STEP 4

Calculate the sum of the constant terms.8.41+3.46=11.87 8.41 + 3.46 = 11.87 8.41+3.46=11.87

STEP 5

Combine the terms with the variable bbb on the left-hand side.3b+3.78b 3b + 3.78b 3b+3.78b

STEP 6

Calculate the sum of the terms with the variable bbb.3b+3.78b=6.78b 3b + 3.78b = 6.78b 3b+3.78b=6.78b

STEP 7

Now, we have the simplified left-hand side of the equation.11.87+6.78b 11.87 + 6.78b 11.87+6.78b

STEP 8

Next, we will express the right-hand side of the equation in a similar form to the left-hand side by filling in the boxes with the appropriate terms.(3b+□)+(8.41+□) (3b + \square) + (8.41 + \square) (3b+□)+(8.41+□)

STEP 9

From the left-hand side, we know the term that combines with 3b3b3b is 6.78b6.78b6.78b and the term that combines with 8.418.418.41 is 11.8711.8711.87.

STEP 10

Fill in the boxes on the right-hand side with the corresponding terms.(3b+6.78b)+(8.41+11.87) (3b + 6.78b) + (8.41 + 11.87) (3b+6.78b)+(8.41+11.87)

STEP 11

Now, we have the right-hand side of the equation expressed with the correct terms.(3b+6.78b)+(8.41+11.87)=11.87+6.78b (3b + 6.78b) + (8.41 + 11.87) = 11.87 + 6.78b (3b+6.78b)+(8.41+11.87)=11.87+6.78b

STEP 12

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Add the expressions in the boxes to simplify the given expressions involving $8.41$ , $3b$ , $3.46$ , and $3.78b$ .

Assumptions
1. The expressions involve real numbers.
2. The expressions on both sides of the equation are equal.
3. We are to simplify and combine like terms.

First, we will combine like terms on the left-hand side of the equation. Like terms are terms that have the same variable raised to the same power.
$(8.41 + 3b) + (3.46 + 3.78b)$

Combine the constant terms (terms without variables) on the left-hand side.
$8.41 + 3.46$

Calculate the sum of the constant terms.
$8.41 + 3.46 = 11.87$

Combine the terms with the variable $b$ on the left-hand side.
$3b + 3.78b$

Calculate the sum of the terms with the variable $b$ .
$3b + 3.78b = 6.78b$

Now, we have the simplified left-hand side of the equation.
$11.87 + 6.78b$

Next, we will express the right-hand side of the equation in a similar form to the left-hand side by filling in the boxes with the appropriate terms.
$(3b + \square) + (8.41 + \square)$

From the left-hand side, we know the term that combines with $3b$ is $6.78b$ and the term that combines with $8.41$ is $11.87$ .

Fill in the boxes on the right-hand side with the corresponding terms.
$(3b + 6.78b) + (8.41 + 11.87)$

Now, we have the right-hand side of the equation expressed with the correct terms.
$(3b + 6.78b) + (8.41 + 11.87) = 11.87 + 6.78b$