(x - 4)(x + 2) = (3x - 5) Quantity A x Quantity B 3
-
Quantity A is greater.
-
Quantity B is greater.
-
The two quantities are equal.
-
The relationship cannot be determined from the information given.
(x-4)(x+2) = x^2 - 2x - 8 = 3x - 5. x^2 - 5x - 3 = 0. Using the quadratic formula, x = (5 +/- sqrt(25 - 4*1*-3)) / 2 = (5 +/- sqrt(37)) / 2. sqrt(37) is between 6 and 7. x1 approx (5+6.08)/2 = 5.54. x2 approx (5-6.08)/2 = -0.54. Since x can be either value, it cannot be determined if x > 3 or x < 3.
Expanding both sides gives x^2 - 2x - 8 = 3x - 5, which simplifies to the quadratic equation x^2 - 5x - 3 = 0. Using the quadratic formula, the roots are x = (5 ± sqrt(25 - (-12))) / 2, which equals (5 ± sqrt(37)) / 2. This results in two distinct values for x, one approximately 5.54 and the other approximately -0.54. Since one value is greater than 3 and the other is less than 3, the relationship cannot be determined.