Questions: Solve the following inequality and graph the solution: (x-1)(x-4) ≥ 0 Write the solution as a compound inequality And draw the solution

Solution Steps

The given inequality is $(x-1)(x-4) \ge 0$. The roots of the quadratic equation $(x-1)(x-4) = 0$ are $x=1$ and $x=4$.

We need to find the values of $x$ for which $(x-1)(x-4) \ge 0$. This inequality holds true when both factors are non-negative or both factors are non-positive.

$(x-1) \ge 0$ and $(x-4) \ge 0$. This means $x \ge 1$ and $x \ge 4$. Both conditions are satisfied when $x \ge 4$.

$(x-1) \le 0$ and $(x-4) \le 0$. This means $x \le 1$ and $x \le 4$. Both conditions are satisfied when $x \le 1$.

The solution to the inequality is $x \le 1$ or $x \ge 4$.

Final Answer: