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

2 min read Jun 17, 2024

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.