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(x+2)(x+3)=(x+1)(x+5)

2 min read Jun 16, 2024
(x+2)(x+3)=(x+1)(x+5)

Solving the Equation (x+2)(x+3) = (x+1)(x+5)

This equation involves expanding brackets and solving for the unknown variable 'x'. Let's break down the steps:

Expanding the Brackets

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

  • Left side: (x+2)(x+3) = x(x+3) + 2(x+3) = x² + 3x + 2x + 6 = x² + 5x + 6
  • Right side: (x+1)(x+5) = x(x+5) + 1(x+5) = x² + 5x + x + 5 = x² + 6x + 5

Now our equation looks like this: x² + 5x + 6 = x² + 6x + 5

Simplifying the Equation

Notice that both sides have the term 'x²'. We can subtract 'x²' from both sides to eliminate it:

  • x² + 5x + 6 - x² = x² + 6x + 5 - x²
  • This simplifies to 5x + 6 = 6x + 5

Isolating 'x'

Now we need to isolate 'x' on one side of the equation. Let's subtract '5x' from both sides:

  • 5x + 6 - 5x = 6x + 5 - 5x
  • This simplifies to 6 = x + 5

Finally, subtract '5' from both sides to get 'x' by itself:

  • 6 - 5 = x + 5 - 5
  • This gives us x = 1

Solution

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

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