Question

Solve the following inequality. x³-x²≦x-16x+16 Write your answer as an interval or union of intervals. If there is no real solution, click on "No solution".

Answer 1

To solve the inequality x³-x²≦x-16x+16, we simplify and combine like terms, factor the quadratic expression, and apply the sign rules to find the intervals where the inequality is true.

Step-by-step explanation:

We have the inequality x³-x²≦x-16x+16. To solve this inequality, we need to simplify and combine like terms. Rearranging the terms, we get x³-x²-17x+16≦0. Now, we can factor the quadratic expression, which gives us (x-16)(x+1)≦0. To find the intervals where the expression is less than or equal to zero, we need to consider the sign of each factor and apply the sign rules. The solutions are: x≤-1 or 16≤x≤17.