5Question: A soil scientist in Iowa measures the productivity of three experimental farm plots over a season, recording yields of $ 3x+4 $, $ 5x-2 $, and $ 4x+7 $ bushels per acre. If the average yield is 22 bushels, what is the value of $ x $?

["<<unlocking farm="" how="" insights="" iowa’s="" math="" powers="" productivity:="" science="" soil="">>", "In a quiet corner of Iowa, a soil scientist diligently tracks seasonal yields from three experimental plots—each capturing a unique expression of soil health and farming innovation. The recorded yields show $3x+4$, $5x-2$, and $4x+7$ bushels per acre, creating a puzzle where mathematics becomes a lens into agricultural potential. With the seasonal average yield hovering at 22 bushels, the question arises: how does this system reveal not just data, but real-world insight? Exploring this intersection of science, math, and farming is gaining attention as agricultural data analysis evolves in rural communities and beyond.", "Why are farmers, agronomists, and agricultural researchers increasingly turning to equations like this? In an era shaped by climate uncertainty and fluctuating commodity prices, optimizing soil productivity is no longer optional—it’s essential. The average yield serves as a critical benchmark, reflecting the interplay of soil quality, weather, crop variety, and management practices. Using algebra to model variable yields transforms raw farm data into actionable intelligence, empowering producers to make informed decisions. This practical application of math fuels growing interest, particularly in regions like Iowa where decades of farming innovation continue to drive progress.", "To find the value of $ x $ that makes the average of these three experimental plots equal to 22 bushels per acre, we start with a simple yet powerful equation. The average of three numbers equals their sum divided by three. So: \n$$\n\frac{(3x + 4) + (5x - 2) + (4x + 7)}{3} = 22\n$$ \nCombining the expressions: \n$$\n\frac{12x + 9}{3} = 22\n$$ \nSimplify the left side: \n$$\n4x + 3 = 22\n$$ \nSolving for $ x $: \n$$\n4x = 19 \quad \Rightarrow \quad x = \frac{"]