(x-1)-(x-4)(x%2B1)%3D6.jpeg "(x-10)(x-1)-(x-4)(x+1)=6")
Solving the Equation (x-10)(x-1)-(x-4)(x+1)=6
This article will guide you through the steps to solve the equation (x-10)(x-1)-(x-4)(x+1)=6.
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) = x(x-1) - 10(x-1) = x² - x - 10x + 10 = x² - 11x + 10
- (x-4)(x+1) = x(x+1) - 4(x+1) = x² + x - 4x - 4 = x² - 3x - 4
Now our equation looks like this:
x² - 11x + 10 - (x² - 3x - 4) = 6
Step 2: Simplify the Equation
Next, we need to simplify the equation by removing the parentheses and combining like terms:
x² - 11x + 10 - x² + 3x + 4 = 6
-8x + 14 = 6
Step 3: Isolate the Variable
Now we need to isolate the variable (x) on one side of the equation. To do this, we can subtract 14 from both sides:
-8x = -8
Step 4: Solve for x
Finally, we can solve for x by dividing both sides by -8:
x = 1
Conclusion
Therefore, the solution to the equation (x-10)(x-1)-(x-4)(x+1)=6 is x = 1.