Which represents the solution set to the inequality \( 5.1(3+2.2 x)>-14.25-6(1.7 x+4) \) ? \( x<-2.5 \) \( x>2.5 \) \( (-2.5, \infty) \) \( (-\infty, 2.5) \)

To solve the inequality \( 5.1(3+2.2 x) > -14.25 - 6(1.7 x+4) \), first distribute the terms on both sides. You'll simplify the left side to \( 15.3 + 11.2 x \) and the right side to \( -14.25 - 10.2 x - 24 \), which combines to \( -38.25 - 10.2 x \). Bringing all \( x \) terms to one side gives us \( 11.2 x + 10.2 x > -38.25 - 15.3 \), which simplifies to \( 21.4 x > -53.55 \). Dividing by \( 21.4 \) results in \( x > 2.5 \). Therefore, the solution set is \( x > 2.5 \). The world of inequalities isn't just about finding limits; it’s the foundation for various applications! For instance, in economics, companies use inequalities to determine profit margins: how much they need to produce to not just break even but actually profit. So dollars, cents, and a touch of algebra can lead to real-world decision-making!