Use algebraic and/or graphical methods to solve the inequality.
- $( x + 4 ) ( x - 4 ) ^ { 2 } > 0$

Question

Use algebraic and/or graphical methods to solve the inequality. -$$( x + 4 ) ( x - 4 ) ^ { 2 } > 0$$ A) $x > - 4$ B) $- 4 < x < - 4$ or $x > - 4$ C) All real numbers D) $- 4 < x < 4$ or $x > 4$

Quizplus · Accepted Answer

To solve the inequality $(x + 4)(x - 4)^2 > 0$, we first find the critical points by setting the expression equal to zero: $x + 4 = 0$ gives $x = -4$, and $(x - 4)^2 = 0$ gives $x = 4$. These are the points where the expression changes sign. Testing intervals around these points (-∞ to -4, -4 to 4, and 4 to ∞), we find that the expression is positive for $x < -4$ and $x > 4$, but because $x = -4$ makes the first part of the expression zero and the second part positive, the correct intervals that satisfy the inequality are $-4 < x < 4$ or $x > 4$.

Use Algebraic And/or Graphical Methods to Solve the Inequality (x+4)(x−4)2>0( x + 4 ) ( x - 4 ) ^ { 2 } > 0(x+4)(x−4)2>0

Use Algebraic And/or Graphical Methods to Solve the Inequality $( x + 4 ) ( x - 4 ) ^ { 2 } > 0$