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(3x+2)(2x+9)-(x+2)(6x+1)=(x+1)-(x-6)

2 min read Jun 16, 2024
(3x+2)(2x+9)-(x+2)(6x+1)=(x+1)-(x-6)

Solving the Equation: (3x+2)(2x+9)-(x+2)(6x+1)=(x+1)-(x-6)

This article will guide you through the process of solving the given equation step-by-step.

1. Expanding the Equation

First, we need to expand the products on both sides of the equation using the FOIL method (First, Outer, Inner, Last).

  • Left Side:
    • (3x+2)(2x+9) = 6x² + 27x + 4x + 18 = 6x² + 31x + 18
    • (x+2)(6x+1) = 6x² + x + 12x + 2 = 6x² + 13x + 2
  • Right Side:
    • (x+1)-(x-6) = x + 1 - x + 6 = 7

2. Simplifying the Equation

Now, we can substitute the expanded terms back into the original equation and simplify:

  • 6x² + 31x + 18 - (6x² + 13x + 2) = 7
  • 6x² + 31x + 18 - 6x² - 13x - 2 = 7

3. Combining Like Terms

Combine the similar terms on the left side of the equation:

  • (6x² - 6x²) + (31x - 13x) + (18 - 2) = 7
  • 18x + 16 = 7

4. Isolating the Variable

Subtract 16 from both sides of the equation:

  • 18x + 16 - 16 = 7 - 16
  • 18x = -9

5. Solving for x

Finally, divide both sides of the equation by 18 to find the value of x:

  • 18x / 18 = -9 / 18
  • x = -1/2

Therefore, the solution to the equation (3x+2)(2x+9)-(x+2)(6x+1)=(x+1)-(x-6) is x = -1/2.

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