Solve the inequality x(x + 6) > 16 - x + 14 + x^2. Write your answer in interval notation.

kelhaku Dec 18, 2023

#1**0 **

We can solve the inequality x(x + 6) > 16 - x + 14 + x^2 by following these steps:

Simplify the right side:

Combining constant terms on the right:

x(x + 6) > 16 + x^2

Expand the left side:

x * (x + 6) = x^2 + 6x

Move all terms to one side:

x^2 + 6x - (x^2 + 6x) > 16

0 > 16 (contradiction)

Analyze the result:

Since we obtain a contradiction (always false statement) after moving all terms to one side, there are no real values of x that satisfy the inequality.

Write the solution in interval notation:

Therefore, the solution is the empty set:

x ∈ ∅

This means there are no intervals which represent the solution, as there are no valid real numbers satisfying the inequality.

BuiIderBoi Dec 18, 2023