Let Juwan's number be represented by \( x \). The problem states that twice the sum of Juwan's number and 12 is equal to four less than three times Juwan's number. We can translate this statement into an equation:
\[ 2(x + 12) = 3x - 4 \]
Now, let's simplify the equation step-by-step.
- Expand the left side:
\[ 2x + 24 = 3x - 4 \]
- Next, move the \( 2x \) term to the right side by subtracting \( 2x \) from both sides:
\[ 24 = 3x - 2x - 4 \]
This simplifies to:
\[ 24 = x - 4 \]
- Now, add 4 to both sides to isolate \( x \):
\[ 24 + 4 = x \]
\[ x = 28 \]
Thus, Juwan is thinking of the number \( \boxed{28} \).
To verify, we can substitute \( x = 28 \) back into the original condition:
- Calculate twice the sum of \( 28 \) and \( 12 \):
\[ 2(28 + 12) = 2 \times 40 = 80 \]
- Calculate four less than three times \( 28 \):
\[ 3 \times 28 - 4 = 84 - 4 = 80 \]
Since both sides are equal (80 = 80), the solution is confirmed. Juwan's number is indeed \( \boxed{28} \).
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