(x-2)(x+3)-(x+4)(x-7)=5-x

2 min read Jun 17, 2024
(x-2)(x+3)-(x+4)(x-7)=5-x

Solving the Equation: (x-2)(x+3)-(x+4)(x-7)=5-x

This article will guide you through solving the algebraic equation: (x-2)(x+3)-(x+4)(x-7)=5-x. We will break down the steps involved in finding the solution for 'x'.

1. Expanding the Equation

First, we need to expand the equation by multiplying the terms in the brackets.

  • (x-2)(x+3): This expands to x² + x - 6
  • (x+4)(x-7): This expands to x² - 3x - 28

Now, the equation becomes: x² + x - 6 - (x² - 3x - 28) = 5 - x

2. Simplifying the Equation

Next, we simplify the equation by removing the parentheses and combining like terms:

  • x² + x - 6 - x² + 3x + 28 = 5 - x
  • 4x + 22 = 5 - x

3. Isolating 'x'

To isolate 'x' on one side of the equation, we need to move all the 'x' terms to one side and the constant terms to the other side.

  • 4x + x = 5 - 22
  • 5x = -17

4. Solving for 'x'

Finally, we solve for 'x' by dividing both sides of the equation by 5:

  • x = -17/5

Therefore, the solution to the equation (x-2)(x+3)-(x+4)(x-7)=5-x is x = -17/5.

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