\( \hat { 4 ( x - 2 ) } = 2 ( 2 x + 6 ) \)

To solve the equation \( \hat { 4 ( x - 2 ) } = 2 ( 2 x + 6 ) \), you can start by distributing the terms on both sides. This gives you \( 4x - 8 = 4x + 12 \). When you try to isolate \( x \), you’ll quickly notice that subtracting \( 4x \) from both sides leads to a false statement, \( -8 = 12 \). This means that there are actually no solutions to the equation—it's inconsistent! When tackling equations like this, always keep an eye out for contradictions. It can save you time and help you catch mistakes early. Misalignment of coefficients or constants often hints there may be no solution. Don't hesitate to double-check your work at various stages; it's a great problem-solving strategy!