Jasonbradley
Home

(8x-3)(3x+2)-(4x+7)(x+4)=(4x+1)(5x-1)

3 min read Jun 16, 2024
(8x-3)(3x+2)-(4x+7)(x+4)=(4x+1)(5x-1)

Solving the Equation: (8x-3)(3x+2)-(4x+7)(x+4)=(4x+1)(5x-1)

This article will guide you through the steps of solving the equation: (8x-3)(3x+2)-(4x+7)(x+4)=(4x+1)(5x-1). We will use the distributive property and algebraic simplification to arrive at the solution.

Expanding the Equation

First, we need to expand each set of parentheses using the distributive property:

  1. (8x-3)(3x+2):

    • 8x * 3x = 24x²
    • 8x * 2 = 16x
    • -3 * 3x = -9x
    • -3 * 2 = -6
    • Combining these terms: 24x² + 16x - 9x - 6 = 24x² + 7x - 6

  2. (4x+7)(x+4):

    • 4x * x = 4x²
    • 4x * 4 = 16x
    • 7 * x = 7x
    • 7 * 4 = 28
    • Combining these terms: 4x² + 16x + 7x + 28 = 4x² + 23x + 28

  3. (4x+1)(5x-1):

    • 4x * 5x = 20x²
    • 4x * -1 = -4x
    • 1 * 5x = 5x
    • 1 * -1 = -1
    • Combining these terms: 20x² - 4x + 5x - 1 = 20x² + x - 1

Now, we can rewrite the original equation with the expanded terms: 24x² + 7x - 6 - (4x² + 23x + 28) = 20x² + x - 1

Simplifying the Equation

Let's simplify the equation by combining like terms:

  1. Distribute the negative sign:

    • 24x² + 7x - 6 - 4x² - 23x - 28 = 20x² + x - 1

  2. Combine the x² terms:

    • 20x² + 7x - 6 - 23x - 28 = 20x² + x - 1

  3. Combine the x terms:

    • 20x² - 16x - 6 - 28 = 20x² + x - 1

  4. Combine the constant terms:

    • 20x² - 16x - 34 = 20x² + x - 1

  5. Move all terms to one side:

    • 20x² - 16x - 34 - 20x² - x + 1 = 0

  6. Simplify further:

    • -17x - 33 = 0

Solving for x

Finally, we can solve for 'x' by isolating it:

  1. Add 33 to both sides:

    • -17x = 33

  2. Divide both sides by -17:

    • x = -33/17

Therefore, the solution to the equation (8x-3)(3x+2)-(4x+7)(x+4)=(4x+1)(5x-1) is x = -33/17.

Featured Posts