(x-5)(x-2)-(x+1)(x-4)=6

2 min read Jun 17, 2024

Solving the Equation: (x-5)(x-2) - (x+1)(x-4) = 6

This article will guide you through the steps to solve the equation (x-5)(x-2) - (x+1)(x-4) = 6. We'll utilize algebraic manipulation to simplify the equation and isolate the variable x.

Expanding the Products

First, we need to expand the products on both sides of the equation:

(x-5)(x-2): Using the distributive property (or FOIL method), we get:
- x² - 2x - 5x + 10 = x² - 7x + 10
(x+1)(x-4): Similarly, we get:
- x² - 4x + x - 4 = x² - 3x - 4

Now, our equation becomes: (x² - 7x + 10) - (x² - 3x - 4) = 6

Simplifying the Equation

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

x² - 7x + 10 - x² + 3x + 4 = 6
-4x + 14 = 6

Isolating the Variable x

To isolate x, we need to perform the following steps:

Subtract 14 from both sides: -4x + 14 - 14 = 6 - 14 -4x = -8
Divide both sides by -4: -4x / -4 = -8 / -4 x = 2

Solution

Therefore, the solution to the equation (x-5)(x-2) - (x+1)(x-4) = 6 is x = 2.