(x%2B1)%3D(x-1)(x%2B3).jpeg "(x-2)(x+1)=(x-1)(x+3)")
Solving the Equation: (x-2)(x+1) = (x-1)(x+3)
This equation involves expanding brackets and simplifying to solve for the unknown variable 'x'. Let's break down the steps:
Expanding the Brackets:
First, we need to expand the brackets on both sides of the equation using the distributive property:
- Left Side: (x-2)(x+1) = x(x+1) - 2(x+1) = x² + x - 2x - 2 = x² - x - 2
- Right Side: (x-1)(x+3) = x(x+3) - 1(x+3) = x² + 3x - x - 3 = x² + 2x - 3
Now our equation becomes: x² - x - 2 = x² + 2x - 3
Simplifying the Equation:
We can simplify the equation by subtracting x² from both sides:
-x - 2 = 2x - 3
Next, let's isolate the 'x' terms on one side:
-3x = -1
Solving for 'x':
Finally, we can solve for 'x' by dividing both sides by -3:
x = 1/3
Therefore, the solution to the equation (x-2)(x+1) = (x-1)(x+3) is x = 1/3.
Verification:
To verify our solution, we can substitute x = 1/3 back into the original equation:
- Left Side: (1/3 - 2)(1/3 + 1) = (-5/3)(4/3) = -20/9
- Right Side: (1/3 - 1)(1/3 + 3) = (-2/3)(10/3) = -20/9
Since both sides equal -20/9, we have verified that our solution x = 1/3 is correct.