(x%2B6)-(x-2)(x-3)%3D3.jpeg "(x-1)(x+6)-(x-2)(x-3)=3")
Solving the Equation (x-1)(x+6)-(x-2)(x-3)=3
This article will guide you through the steps of solving the equation (x-1)(x+6)-(x-2)(x-3)=3.
Expanding the Equation
First, we need to expand the equation by multiplying out the brackets:
- (x-1)(x+6) = x² + 6x - x - 6 = x² + 5x - 6
- (x-2)(x-3) = x² - 3x - 2x + 6 = x² - 5x + 6
Now, substitute these expanded terms back into the original equation:
x² + 5x - 6 - (x² - 5x + 6) = 3
Simplifying the Equation
Next, we simplify the equation by removing the parentheses and combining like terms:
x² + 5x - 6 - x² + 5x - 6 = 3 10x - 12 = 3
Isolating the Variable
To solve for 'x', we need to isolate the variable by adding 12 to both sides of the equation:
10x = 15
Solving for 'x'
Finally, we divide both sides of the equation by 10 to get the solution for 'x':
x = 15/10 x = 1.5
Therefore, the solution to the equation (x-1)(x+6)-(x-2)(x-3)=3 is x = 1.5.