Fill in the blank: \( 4(3 x-2)=\_x-8 \) *

To solve the equation \( 4(3x - 2) = \_x - 8 \), first distribute the 4 on the left side: \( 12x - 8 = \_x - 8 \). Now, to maintain balance, recognize that both sides already have "-8", so we can add 8 to both sides: \( 12x = \_x \). At this point, we can see that the coefficients of \( x \) should match on both sides, leading us to conclude that: \_ = 12. Thus, we fill the blank with "12" to complete the equation! Problem-solving tip: Always maintain balance in equations by performing the same operation to both sides. This principle helps avoid common mistakes like losing track of terms.