(2x-1)(x-2)-(x+3)(2x-7)=3

2 min read Jun 16, 2024

Solving the Equation (2x-1)(x-2)-(x+3)(2x-7)=3

This article will guide you through the process of solving the equation (2x-1)(x-2)-(x+3)(2x-7)=3. We will utilize algebraic manipulations to isolate the variable x and arrive at the solution(s).

Expanding the Equation

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

(2x-1)(x-2) = 2x² - 4x - x + 2 = 2x² - 5x + 2
(x+3)(2x-7) = 2x² - 7x + 6x - 21 = 2x² - x - 21

Now, the equation becomes: (2x² - 5x + 2) - (2x² - x - 21) = 3

Simplifying the Equation

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

2x² - 2x² = 0
-5x + x = -4x
2 + 21 = 23

The equation is now: -4x + 23 = 3

Isolating the Variable

To isolate x, we subtract 23 from both sides of the equation:

-4x = -20

Finally, we divide both sides by -4 to get the value of x:

x = 5

Conclusion

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