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(x-1)(2x-3)-(x+3)(2x-5)=4

less than a minute read Jun 17, 2024
(x-1)(2x-3)-(x+3)(2x-5)=4

Solving the Equation: (x-1)(2x-3)-(x+3)(2x-5)=4

This article will guide you through the steps to solve the given equation.

Expanding the Equation

First, we need to expand the equation by multiplying out the brackets:

  • (x-1)(2x-3):
    • 2x² - 3x - 2x + 3 = 2x² - 5x + 3
  • (x+3)(2x-5):
    • 2x² - 5x + 6x - 15 = 2x² + x - 15

Now, the equation becomes: (2x² - 5x + 3) - (2x² + x - 15) = 4

Simplifying the Equation

Next, we can simplify the equation by combining like terms:

  • 2x² - 5x + 3 - 2x² - x + 15 = 4
  • -6x + 18 = 4

Solving for x

Now, we need to isolate the variable 'x' to solve for its value:

  • -6x = 4 - 18
  • -6x = -14
  • x = -14 / -6
  • x = 7/3

Conclusion

Therefore, the solution to the equation (x-1)(2x-3)-(x+3)(2x-5)=4 is x = 7/3.

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