Final answer:
To solve the equation (3x - 2)(x + 1) = 3(x + 4)(x - 1), we expand, simplify, and rearrange the terms to solve for x, resulting in x = 1/8. We then check the answer to confirm its validity.
Step-by-step explanation:
The equation we need to solve is (3x - 2)(x + 1) = 3(x + 4)(x - 1). To solve for x, we first expand both sides:
3x2 + 3x - 2x - 2 = 3x2 + 12x - 3x - 12.
After simplifying, we get:
x + (-2) = 9x - 12.
Now we can eliminate terms and bring all x terms to one side and constants to the other:
x - 9x = -12 + 2.
-8x = -10.
Finally, we divide by -8 to solve for x:
x = ⅓
It's important to check the answer to ensure it makes original equation true. We substitute x = ⅓ into the original equation:
(3(⅓) - 2)((⅓) + 1) ≈ 3((⅓) + 4)((⅓) - 1).
The simplification on both sides should result in the same value, confirming the solution x = ⅓ is correct.