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Solved on Jan 30, 2024

Find the missing value in the equation 12x+□=4(3x+3)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+□=4(3x+3)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⋅3x+4⋅34(3x + 3) = 4 \cdot 3x + 4 \cdot 3

STEP 3

Now, perform the multiplication to simplify the expression.
4⋅3x=12x4 \cdot 3x = 12x 4⋅3=124 \cdot 3 = 12

STEP 4

Combine the results from the multiplication to rewrite the right side of the equation.
4(3x+3)=12x+124(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+□=12x+1212x + \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 xx 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.
□=12\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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