(x-10)(x-1)-(x+1)(x-4)=6

2 min read Jun 17, 2024

Solving the Equation: (x-10)(x-1)-(x+1)(x-4)=6

This article will guide you through the process of solving the equation (x-10)(x-1)-(x+1)(x-4)=6. We will utilize algebraic manipulation to isolate the variable x and determine its value.

Step 1: Expand the Products

First, we need to expand the products on both sides of the equation. We can do this by using the distributive property (also known as FOIL method):

(x-10)(x-1): x² - x - 10x + 10
(x+1)(x-4): x² - 4x + x - 4

Now, the equation becomes: (x² - x - 10x + 10) - (x² - 4x + x - 4) = 6

Step 2: Simplify the Equation

Combining like terms on the left side of the equation:

x² - 11x + 10 - x² + 3x + 4 = 6

This simplifies to:

-8x + 14 = 6

Step 3: Isolate the Variable

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

Subtracting 14 from both sides:

-8x = -8

Step 4: Solve for x

Finally, we can solve for x by dividing both sides of the equation by -8:

x = 1

Solution

Therefore, the solution to the equation (x-10)(x-1)-(x+1)(x-4)=6 is x = 1.