Let \( x \) be the number Juwan is thinking of. According to the problem, we can translate the statements into an equation.
Twice the sum of Juwan's number and 12 can be expressed as: \[ 2(x + 12) \] Three times Juwan's number can be expressed as: \[ 3x \] The problem states that twice the sum of Juwan's number and 12 is equal to four less than three times Juwan's number. Therefore, we can write the equation: \[ 2(x + 12) = 3x - 4 \]
Now, we will simplify this equation step-by-step.
First, distribute the \( 2 \) on the left side: \[ 2x + 24 = 3x - 4 \]
Next, to isolate the variable, we will subtract \( 2x \) from both sides: \[ 24 = 3x - 2x - 4 \] This simplifies to: \[ 24 = x - 4 \]
Now, add \( 4 \) to both sides to solve for \( x \): \[ 24 + 4 = x \] \[ x = 28 \]
Thus, the number Juwan is thinking of is: \[ \boxed{28} \]
To ensure our solution is correct, we can substitute \( x = 28 \) back into the original conditions and verify.
First, calculate \( 2(x + 12) \): \[ 2(28 + 12) = 2(40) = 80 \]
Next, calculate \( 3x - 4 \): \[ 3(28) - 4 = 84 - 4 = 80 \]
Since both expressions equal \( 80 \), our solution is confirmed: \[ \boxed{28} \]