What was causing economic booms in the north and south

But shortly after arriving, he found that planters throughout the South—including his new employer—weren't doing too hot financially.

Tobacco, the cash crop that had sustained the Southern economy for over a century, had fallen sharply in value.

The South's other exports, like rice, corn, wheat, and indigo, weren't profitable enough to cover the steep costs of land, supplies, and slave labor.

Some plantations attempted to grow cotton, which Europe and the textile mills in the North were increasingly demanding. But besides a few isolated regions, only the green seed variety thrived, and cotton required a full day of manual labor to separate a handful of the soft lint from several pounds of tiny, coarse seeds. The price of slave labor far exceeded any money that could be made cultivating the troublesome product.

Being the Ivy League grad he was, Whitney studied the meticulous work of the few Savannah slaves who cleaned green seed cotton. Then he developed a mechanical device that could replicate the movement of their fingers.

His invention, the cotton gin, was a simple contraption featuring a series of rotating cylinders fitted with wires and brushes that rapidly captured the lint and discarded the seeds. In a single hour, Whitney's machine accomplished more than a team of laborers completed in a full day. Within just one decade the new device had revolutionized cotton production throughout the South.

for this case we have the following equation:

we apply distributive property to the terms within parentheses.

subtracting 2 on both sides of the equation:

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