Please describe and correct the error.
(3x-2(2x-3)= 3x(2x-3)-2(2x-3)=6x^2-9x-4x-6=6x^2-13x-6
Thank you for your help.
(3x-2(2x-3)) = 3x-4x-6 = -x+6
Error is in first step: misapplication of distributive function.
without the typo, we have
(3x-2)(2x-3)
= 3x(2x-3) - 2(2x-3)
= 6x^2-9x - (4x-6)
= 6x^2-9x - 4x+6 <-------
= 6x^2-13x+6
The given equation is:
(3x - 2(2x - 3)) = 3x(2x - 3) - 2(2x - 3) = 6x^2 - 9x - 4x - 6 = 6x^2 - 13x - 6
Let's simplify and correct the error in this equation step by step:
Step 1: Distribute the negative sign to the terms inside the bracket:
(3x - 4x + 6) = 6x^2 - 9x - 4x - 6
Step 2: Simplify both sides of the equation:
-x + 6 = 6x^2 - 13x - 6
Step 3: Move all terms to one side to have a quadratic equation in standard form:
6x^2 - 12x - 13x + x - 6 - 6 = 0
6x^2 - 12x - 12x - 6 = 0
6x^2 - 24x - 6 = 0
The corrected equation is:
6x^2 - 24x - 6 = 0