Solved on Jan 30, 2024

# Find the missing value in the equation $12x + \square = 4(3x + 3)$.

#### STEP 1

### Assumptions

1. We are given an equation with a missing number represented by a square.

2. The equation is of the form $12x + \square = 4(3x + 3)$.

3. We need to find the value of the missing number that makes the equation true.

#### STEP 2

### First, we need to simplify the right side of the equation by distributing the 4 into the parentheses.

$4(3x + 3) = 4 \cdot 3x + 4 \cdot 3$

#### STEP 3

### Now, perform the multiplication to simplify the expression.

$4 \cdot 3x = 12x$
$4 \cdot 3 = 12$

#### STEP 4

### Combine the results from the multiplication to rewrite the right side of the equation.

$4(3x + 3) = 12x + 12$

#### STEP 5

### Now that we have simplified the right side, we can rewrite the original equation with the simplified expression.

$12x + \square = 12x + 12$

#### STEP 6

### To find the missing number, we need to compare the left side of the equation to the right side. Since the terms with $x$ are identical on both sides, we can focus on the constants.

#### STEP 7

### The missing number must be equal to the constant on the right side of the equation for the equation to be true.

$\square = 12$

#### STEP 8

### We have found the value of the missing number that makes the equation true.

The missing number is 12.

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