(x+1)(x+5)=(x+3)(x-4)+3

2 min read Jun 16, 2024

Solving the Equation: (x+1)(x+5) = (x+3)(x-4) + 3

This article will guide you through the steps of solving the given equation: (x+1)(x+5) = (x+3)(x-4) + 3. We will use algebraic manipulation to isolate the variable x.

Step 1: Expanding both sides

First, we expand both sides of the equation using the distributive property (FOIL method).

Left side: (x+1)(x+5) = x² + 6x + 5
Right side: (x+3)(x-4) + 3 = x² - x - 12 + 3 = x² - x - 9

Now, our equation becomes: x² + 6x + 5 = x² - x - 9

Step 2: Simplifying the equation

Notice that we have x² on both sides of the equation. Subtracting x² from both sides cancels it out:

6x + 5 = -x - 9

Step 3: Combining x terms

To get all x terms on one side, add x to both sides:

7x + 5 = -9

Step 4: Isolating the x term

Subtract 5 from both sides:

7x = -14

Step 5: Solving for x

Finally, divide both sides by 7:

x = -2

Conclusion

Therefore, the solution to the equation (x+1)(x+5) = (x+3)(x-4) + 3 is x = -2.