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(x+4)(x+6)=(x+1)(x+12)

2 min read Jun 16, 2024
(x+4)(x+6)=(x+1)(x+12)

Solving the Equation (x+4)(x+6) = (x+1)(x+12)

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

1. Expand the Brackets

  • Left-hand side:
    • (x+4)(x+6) = x(x+6) + 4(x+6) = x² + 6x + 4x + 24 = x² + 10x + 24
  • Right-hand side:
    • (x+1)(x+12) = x(x+12) + 1(x+12) = x² + 12x + x + 12 = x² + 13x + 12

2. Simplify the Equation

Now our equation becomes: x² + 10x + 24 = x² + 13x + 12

3. Solve for 'x'

  • Subtract x² from both sides: 10x + 24 = 13x + 12
  • Subtract 10x from both sides: 24 = 3x + 12
  • Subtract 12 from both sides: 12 = 3x
  • Divide both sides by 3: x = 4

Solution

Therefore, the solution to the equation (x+4)(x+6) = (x+1)(x+12) is x = 4.

Verification: We can substitute x = 4 back into the original equation to verify our answer:

  • (4+4)(4+6) = (4+1)(4+12)
  • (8)(10) = (5)(16)
  • 80 = 80

This confirms that our solution x = 4 is correct.

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