Let's solve the problem step-by-step and find the value needed to balance the equation.
Given:
[tex]\[
(3 \times 6) \times 2 = 3 \times \Box \times 2 = 3 \times \Box
\][/tex]
First, we simplify the left-hand side of the equation:
[tex]\[
(3 \times 6) \times 2
\][/tex]
Step 1: Calculate [tex]\(3 \times 6\)[/tex]:
[tex]\[
3 \times 6 = 18
\][/tex]
Step 2: Now multiply the result by 2:
[tex]\[
18 \times 2 = 36
\][/tex]
Therefore, the expression simplifies to:
[tex]\[
36
\][/tex]
We now need to express this result as:
[tex]\[
3 \times \Box \times 2
\][/tex]
Let's denote the unknown value by [tex]\( x \)[/tex]:
[tex]\[
3 \times x \times 2
\][/tex]
Since we already know the result needs to equal 36, let's set up the equation:
[tex]\[
3 \times x \times 2 = 36
\][/tex]
To find [tex]\( x \)[/tex], we solve for [tex]\( x \)[/tex] in the equation:
[tex]\[
3 \times x \times 2 = 36
\][/tex]
Step 3: Divide both sides of the equation by 3:
[tex]\[
x \times 2 = 12
\][/tex]
Step 4: Now, divide both sides of the equation by 2:
[tex]\[
x = 6
\][/tex]
Hence, the final value:
[tex]\[
3 \times 6 \times 2 = 36
\][/tex]
The value that [tex]\( \Box \)[/tex] represents is 6.
To summarize, the solved equation is:
[tex]\[
(3 \times 6) \times 2 = 3 \times 6 \times 2 = 36
\][/tex]
Here,
[tex]\(\Box = 6\)[/tex] and [tex]\(\Box = 6\)[/tex], thus [tex]\(3 \times 6 = 36\)[/tex].
The balanced equations are:
[tex]\[
(3 \times 6) \times 2 = 3 \times 6 \times 2 = 3 \times 12 = 36
\][/tex]
