(x%2B3)%3D(x%2B5)(x%2B4).jpeg "(x+6)(x+3)=(x+5)(x+4)")
Solving the Equation: (x+6)(x+3) = (x+5)(x+4)
This equation involves expanding brackets and simplifying to find the value of 'x'. Let's break down the steps:
1. Expand the Brackets
We'll use the distributive property (also known as FOIL) to expand the brackets on both sides of the equation:
- Left side: (x+6)(x+3) = x(x+3) + 6(x+3) = x² + 3x + 6x + 18
- Right side: (x+5)(x+4) = x(x+4) + 5(x+4) = x² + 4x + 5x + 20
Now our equation looks like this: x² + 3x + 6x + 18 = x² + 4x + 5x + 20
2. Simplify by Combining Like Terms
On each side, combine the terms with 'x' and the constant terms:
- Left side: x² + 9x + 18
- Right side: x² + 9x + 20
Our equation is now: x² + 9x + 18 = x² + 9x + 20
3. Solve for 'x'
Notice that the terms x² and 9x appear on both sides. Subtracting x² and 9x from both sides, we get:
18 = 20
This statement is not true. Therefore, there is no solution to the equation (x+6)(x+3) = (x+5)(x+4).
Conclusion
The equation (x+6)(x+3) = (x+5)(x+4) leads to a contradiction, indicating that there is no value of 'x' that satisfies the equation.