6
algebra

Solve: x24x5<0x^2 - 4x - 5 < 0 (Non-linear preview)

A

1<x<5-1 < x < 5

B

x<1x < -1 or x>5x > 5

C

5<x<1-5 < x < 1

D

x<5x < -5 or x>1x > 1

Correct Answer: A

Choice A is the correct answer. Factor and test intervals.

  1. Factor: (x5)(x+1)<0(x - 5)(x + 1) < 0
  2. Roots: x=5,x=1x = 5, x = -1
  3. Test Intervals:
    • x<1x < -1: Neg ×\times Neg = Pos (>0>0)
    • 1<x<5-1 < x < 5 (e.g., 0): Neg ×\times Pos = Neg (<0<0) ??n - x>5x > 5: Pos ×\times Pos = Pos (>0>0)
  4. Result: 1<x<5-1 < x < 5

?�� Strategic Tip: "Less than" for a parabola opening up is the region "between" the roots.

Choice B is incorrect because it describes the outside region (>0>0). Choice C is incorrect because it has wrong roots. Choice D is incorrect because it has wrong roots.