\( 3(x-2)=-4(4+3 x)+15 x \) Conditional Identity

To solve the equation \( 3(x-2)=-4(4+3 x)+15 x \), first simplify both sides. Distributing on the left gives \( 3x - 6 \). For the right side, distribute the \(-4\) to get \(-16 - 12x + 15x\), which simplifies to \(-16 + 3x\). Now, set the two sides equal: \( 3x - 6 = -16 + 3x \). Subtract \(3x\) from both sides, resulting in \(-6 = -16\), which is false, indicating that there are no solutions—it’s not conditional or identity; it's inconsistent! When faced with equations that lead to inconsistencies like this, think of it as a bit of mathematical detective work! Remember, equations can sometimes be like puzzle pieces that just don’t fit together! For further learning, try experimenting with different types of linear equations. Understanding variations, including ones that yield identities or consistent relationships, really enhances your algebra skills!