(x-1)(x+7)=(x+1)(x-3)

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x-1)(x+7) = (x+1)(x-3)

This article will guide you through solving the equation (x-1)(x+7) = (x+1)(x-3).

Expanding the Equation

First, we need to expand both sides of the equation by using the distributive property (also known as FOIL):

• Left side: (x-1)(x+7) = x(x+7) - 1(x+7) = x² + 7x - x - 7 = x² + 6x - 7
• Right side: (x+1)(x-3) = x(x-3) + 1(x-3) = x² - 3x + x - 3 = x² - 2x - 3

Now, our equation looks like this: x² + 6x - 7 = x² - 2x - 3

Simplifying the Equation

To simplify, we can subtract x² from both sides:

6x - 7 = -2x - 3

Next, add 2x to both sides:

8x - 7 = -3

Then, add 7 to both sides:

8x = 4

Solving for x

Finally, divide both sides by 8:

x = 1/2

Conclusion

Therefore, the solution to the equation (x-1)(x+7) = (x+1)(x-3) is x = 1/2.