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

2 min read Jun 16, 2024
(x+1)(x-7)=(x-1)(x+3)

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

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

Expanding the Equation

The first step is to expand both sides of the equation by using the distributive property (also known as FOIL - First, Outer, Inner, Last):

  • 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 and Solving

Next, we want to simplify the equation and solve for x.

  1. Subtract x² from both sides: This eliminates the squared term, leaving us with: -6x - 7 = 2x - 3

  2. Add 6x to both sides: This isolates the x term on the right side: -7 = 8x - 3

  3. Add 3 to both sides: This isolates the x term: -4 = 8x

  4. Divide both sides by 8: This solves for x: x = -1/2

Conclusion

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

This means that if you substitute -1/2 for x in the original equation, both sides of the equation will be equal.

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